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Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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24 Apr 2008, 17:42
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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13 Jun 2010, 03:41
gautamsubrahmanyam wrote: I understand that 1) is insuff
But for 2) xx > 0 means x cant be +ve => x = x so that x (x) = x^2> 0
If x is ve => (x3)^2 = X^2+96x = (ve)^2+96(ve) = +ve+9(ve) = +ve +9 + (+ve) = +ve
=> sqrt ((x3)^2) = +X3
=> sqrt ( (x3) ^2 ) is not equal to 3x
=> Option B
Am I right In my logic.Please help Yes, the answer for this question is B. Is \(\sqrt{(x3)^2}=3x\)? Remember: \(\sqrt{x^2}=x\). Why? Couple of things: The point here is that square root function cannot give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:So \(\sqrt{(x3)^2}=x3\) and the question becomes is: \(x3=3x\)? When \(x>3\), then RHS (right hand side) is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true. When \(x\leq{3}\), then \(LHS=x3=x+3=3x=RHS\), hence in this case equation holds true. Basically question asks is \(x\leq{3}\)? (1) \(x\neq{3}\). Clearly insufficient. (2) \(xx >0\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient. Answer: B. Hope it helps.
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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24 Apr 2008, 21:45
From the que: 3x is always >0 > x has to be less than 3.
Option 1: X can also be >3 when ans fails so insufficient Option 2: xx>0 implies x is always < 0 which means x is less than 3 hence sufficient.
Ans : B




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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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25 Apr 2008, 00:23
gmatnub wrote: is sqrt ((x3)^2) = 3x?
1) x not equal to 3 2) xx > 0
The oa is B, but why is A alone not enough? given x3 can be equal to 3x for x < 3, 1) X can be greater than 3 2) X is less than 0, i.e x < 3, for all x. so B



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Re: gmat prep_inequality
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28 Mar 2010, 12:38
One important thing to know about the square root of a square term: (1) If it's a number under the square root sign, the answer is only the positive root: sqrt[(3)^2] = sqrt[(3)^2] = sqrt[9] = 3. (2) If there are variables under the square root sign, you must consider the fact that the squared "thing" may have been either pos or neg to begin with: sqrt[(x)^2] = sqrt[(x)^2] = x. We are still looking for the positive root, but we don't know whether +x or x is actually greater than zerothat depends on the sign of x. So for this question: Is sqrt[(x3)^2] = 3x? Rephrase to: Is x3 = 3x? If stuff in the absolute value sign is positive or zero, this becomes: Is x3 = 3x? Is 2x = 6? Is x = 3? If stuff in the absolute value sign is negative, this becomes: Is (x3) = 3x? Is x+3 = 3x? The answer is yes for all x, but remember this was just "all x" such that x3 was negative, or x < 3: So we ask "Is x < 3?" Put the two cases together for the final rephrase: "Is x =<3 ? "(1) x is not 3, but no info on whether it is less than or greater than 3. INSUFF. (2) xx > 0. x is positive, so x would have to be positive too (pos*pos > 0, but neg*pos < 0). Thus, x is negative. If x is negative, it is definitely less than 3. The answer is definitely Yes. SUFF. The answer is B.
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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13 Jun 2010, 02:57
I understand that 1) is insuff
But for 2) xx > 0 means x cant be +ve => x = x so that x (x) = x^2> 0
If x is ve => (x3)^2 = X^2+96x = (ve)^2+96(ve) = +ve+9(ve) = +ve +9 + (+ve) = +ve
=> sqrt ((x3)^2) = +X3
=> sqrt ( (x3) ^2 ) is not equal to 3x
=> Option B
Am I right In my logic.Please help



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Re: Is [m][square_root](x  3)[/square_root]^2[/m] = 3  x
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24 Jul 2011, 23:47
Lets disect the question stem first. sqrt((x3)^2) = 3  x Carrying out the squaring and then the square root operation, we get: (x3) = 3  x To solve the modulus sign, we will have two cases  Case 1: (x3)>=0 => x = 3 Case 2: (x3) < 0=> Every value of x less than 3 satisfies the equation Therefore sqrt((x3)^2) = 3  x for all values of x<=3, but this equation is not satisfied for values of x>3 Now consider the statements of the DS. Statement (1): x is not equal to 3If x is not equal to 3, it could be greater than 3 or less than 3. If x is less than 3, the equation is satisfied. If x is greater than 3, the equation is not satisfied. Therefore we cannot say if the equation will be satisfied if x is not equal to 3. Statement (1) alone is therefore insufficient to answer the question. Next lets consider statement (2):Statement (2): xx>0 Again to remove the modulus sign make two cases. Case 1: x>=0 => x(x) >0 => (x^2) > 0, which is impossible because x^2 is always >=0, so (x^2) cannot be >0 for any values of x. Therefore to satisfy this inequality, x cannot be >0 Case 2: x<0 => x (x) > 0 => x^2 > 0 , which is true for all values of x except 0. Therefore the inequality is satisfied for all values of x<0 Therefore from statement (2) we know that x<0. And from the stem of the question (after we solved it), we know that the equation given in the stem is satisfied for all values of x<=3. Therefore the equation will hold for all values of x specified by statement (2). Therefore statement (2) alone is enough to solve the question. The answer is therefore (B).
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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23 Sep 2013, 08:09
Hello Bunuel, Please help me understand where I am going wrong. After this point.. \(x3=3x\) Can this equation be written this way? 1) x3 = 3x => x = 3 2) (x3) = 3x .. this leads to nothing So I concluded that the question is whether x=3 and hence I chose A as answer.. but I am wrong. What is that I doing wrong here? Thanks C23678 Bunuel wrote: Yes, the answer for this question is B.
Is \(\sqrt{(x3)^2}=3x\)?
Remember: \(\sqrt{x^2}=x\). Why?
Couple of things:
The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\).
So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?
Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\).
So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\).
What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\)
Back to the original question:
So \(\sqrt{(x3)^2}=x3\) and the question becomes is: \(x3=3x\)?
When \(x>3\), then RHS (right hand side) is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.
When \(x\leq{3}\), then \(LHS=x3=x+3=3x=RHS\), hence in this case equation holds true.
Basically question asks is \(x\leq{3}\)?
(1) \(x\neq{3}\). Clearly insufficient.
(2) \(xx >0\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient.
Answer: B.
Hope it helps.



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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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24 Sep 2013, 07:22
c23678 wrote: Hello Bunuel, Please help me understand where I am going wrong. After this point.. \(x3=3x\) Can this equation be written this way? 1) x3 = 3x => x = 3 2) (x3) = 3x .. this leads to nothing So I concluded that the question is whether x=3 and hence I chose A as answer.. but I am wrong. What is that I doing wrong here? Thanks C23678 Bunuel wrote: Yes, the answer for this question is B.
Is \(\sqrt{(x3)^2}=3x\)?
Remember: \(\sqrt{x^2}=x\). Why?
Couple of things:
The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\).
So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?
Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\).
So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\).
What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\)
Back to the original question:
So \(\sqrt{(x3)^2}=x3\) and the question becomes is: \(x3=3x\)?
When \(x>3\), then RHS (right hand side) is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.
When \(x\leq{3}\), then \(LHS=x3=x+3=3x=RHS\), hence in this case equation holds true.
Basically question asks is \(x\leq{3}\)?
(1) \(x\neq{3}\). Clearly insufficient.
(2) \(xx >0\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient.
Answer: B.
Hope it helps. \(x3=(x3)\) when \(x\leq{3}\). In this case we'd have \((x3)=3x\) > 3=3 > true. This means that when \(x\leq{3}\), then the equation holds true. Try numbers less than or equal to 3 to check.
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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27 Jul 2014, 10:29
Please clarify a doubt which i have in this question :
If we have a question, Is x<=5, A. X<0 B. X<=0
What will be the answer?
In the original question, I am confused because 0, which satisfies the equation, doesn't appear in xx < 0. And hence the solution is incomplete.



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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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27 Jul 2014, 14:50
vibsaxena wrote: Please clarify a doubt which i have in this question :
If we have a question, Is x<=5, A. X<0 B. X<=0
What will be the answer?
In the original question, I am confused because 0, which satisfies the equation, doesn't appear in xx < 0. And hence the solution is incomplete. The answer would be D. The original question asks whether \(x\leq{3}\): the answer would be YES if x is 3 or less than 3. (2) says that \(x<0\), so the answer is clearly YES. Does this make sense?
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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03 Sep 2014, 12:18
gmatnub wrote: Is \(\sqrt{(x3)^2} = 3x\)?
(1) \(x\neq{3}\) (2) xx > 0 mod(x3)=3x? mod(y) = y when y is ve => mod(x3) can be equal to (x3) only when x3 is negative i.e x3<0 => x<3 1) x not equal to 3=> which means x can be greater than 3 or less than 3 2) xx>0=> this is possible only when x is ve i.e x<0 statement 2 gives x<0, so statement 2 alone solves the problem.



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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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23 Oct 2014, 23:40
Hi BunuelI am still confused about this.Please help me out. As a^2 = 25 has two solutions > a=5 and a= 5 therefore a= sqrt 25 should also have two solutions> a=5 and a= 5 Then why do we say that square root of a positive no. is always positive? Shouldn't sqrt 25 have two possible values +5 and 5. ?



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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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24 Oct 2014, 03:21
arpitsharms wrote: Hi BunuelI am still confused about this.Please help me out. As a^2 = 25 has two solutions > a=5 and a= 5 therefore a= sqrt 25 should also have two solutions> a=5 and a= 5 Then why do we say that square root of a positive no. is always positive? Shouldn't sqrt 25 have two possible values +5 and 5. ? NO! When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root.That is: \(\sqrt{9} = 3\), NOT +3 or 3; \(\sqrt[4]{16} = 2\), NOT +2 or 2; Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and 3. Because \(x^2 = 9\) means that \(x =\sqrt{9}=3\) or \(x=\sqrt{9}=3\). Hope it's clear.
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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22 Nov 2014, 03:02
Bunuel wrote: gautamsubrahmanyam wrote: I understand that 1) is insuff
But for 2) xx > 0 means x cant be +ve => x = x so that x (x) = x^2> 0
If x is ve => (x3)^2 = X^2+96x = (ve)^2+96(ve) = +ve+9(ve) = +ve +9 + (+ve) = +ve
=> sqrt ((x3)^2) = +X3
=> sqrt ( (x3) ^2 ) is not equal to 3x
=> Option B
Am I right In my logic.Please help Yes, the answer for this question is B. Is \(\sqrt{(x3)^2}=3x\)? Remember: \(\sqrt{x^2}=x\). Why? Couple of things: The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:So \(\sqrt{(x3)^2}=x3\) and the question becomes is: \(x3=3x\)? When \(x>3\), then RHS (right hand side) is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true. When \(x\leq{3}\), then \(LHS=x3=x+3=3x=RHS\), hence in this case equation holds true. Basically question asks is \(x\leq{3}\)? (1) \(x\neq{3}\). Clearly insufficient. (2) \(xx >0\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient. Answer: B. Hope it helps. can u pls help in decoding option B where , you say x <0 i mean xx> 0 , could you elaborate on this . thanks.



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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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22 Nov 2014, 07:20
hanschris5 wrote: Bunuel wrote: gautamsubrahmanyam wrote: I understand that 1) is insuff
But for 2) xx > 0 means x cant be +ve => x = x so that x (x) = x^2> 0
If x is ve => (x3)^2 = X^2+96x = (ve)^2+96(ve) = +ve+9(ve) = +ve +9 + (+ve) = +ve
=> sqrt ((x3)^2) = +X3
=> sqrt ( (x3) ^2 ) is not equal to 3x
=> Option B
Am I right In my logic.Please help Yes, the answer for this question is B. Is \(\sqrt{(x3)^2}=3x\)? Remember: \(\sqrt{x^2}=x\). Why? Couple of things: The point here is that square root function can not give negative result: wich means that \(\sqrt{some \ expression}\geq{0}\). So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to? Let's consider following examples: If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\); If \(x=5\) > \(\sqrt{x^2}=\sqrt{25}=5=x=positive\). So we got that: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). What function does exactly the same thing? The absolute value function! That is why \(\sqrt{x^2}=x\) Back to the original question:So \(\sqrt{(x3)^2}=x3\) and the question becomes is: \(x3=3x\)? When \(x>3\), then RHS (right hand side) is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true. When \(x\leq{3}\), then \(LHS=x3=x+3=3x=RHS\), hence in this case equation holds true. Basically question asks is \(x\leq{3}\)? (1) \(x\neq{3}\). Clearly insufficient. (2) \(xx >0\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient. Answer: B. Hope it helps. can u pls help in decoding option B where , you say x <0 i mean xx> 0 , could you elaborate on this . thanks. Sure. We have that \(xx >0\), so the product of two multiples x and x is positive. Now, we know that x must be positive, hence x must also be positive for the product to be positive, thus x > 0, which is the same as x < 0. Hope it's clear.
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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26 Jan 2017, 19:55
Be definition: √(x²) = x. xy is the DISTANCE between x and y. The DISTANCE between two numbers must be greater than or equal to 0. The question stem above, rephrased: Is x3 = 3x? In words: Is the DISTANCE between x and 3 equal to the DIFFERENCE of 3 and x? The answer will be YES if the DIFFERENCE of 3 and x is greater than or equal to 0: 3x≥0 x≤3. The question stem rephrased: Is x≤3? Statement 1: x is not equal to 3. It is possible that x<3 or that x>3. INSUFFICIENT. Statement 2: x*x > 0 . Thus, the lefthand side must be positive*positive or negative*negative. Since x cannot be negative, both factors on the lefthand side must be positive. Thus: x>0 x<0. Since x<0, we know that x≤3. SUFFICIENT. The correct answer is B.
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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02 Oct 2018, 11:30
Bunuel, Thanks for the explanation, but i had one question. You mentioned : "Couple of things: The point here is that square root function can not give negative result: wich means that some expression−−−−−−−−−−−−−−√≥0some expression≥0." Can you please let me know why? Because in general square root gives two values, one positive and one negative.



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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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02 Oct 2018, 20:35
PriyankaGehlawat wrote: Bunuel, Thanks for the explanation, but i had one question. You mentioned : "Couple of things: The point here is that square root function can not give negative result: wich means that some expression−−−−−−−−−−−−−−√≥0some expression≥0." Can you please let me know why? Because in general square root gives two values, one positive and one negative. \(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means nonnegative square root. The graph of the function f(x) = √xNotice that it's defined for nonnegative numbers and is producing nonnegative results. TO SUMMARIZE: When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the nonnegative root. That is: \(\sqrt{9} = 3\), NOT +3 or 3; \(\sqrt[4]{16} = 2\), NOT +2 or 2; Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and 3. Because \(x^2 = 9\) means that \(x =\sqrt{9}=3\) or \(x=\sqrt{9}=3\).
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Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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04 Jun 2019, 10:05
Dear Brunel,
You said
"Is (x−3)2−−−−−−−√=3−x(x−3)2=3−x?
Remember: x2−−√=xx2=x. Why?
Couple of things:
The point here is that square root function can not give negative result: wich means that some expression−−−−−−−−−−−−−−√≥0some expression≥0.
So x2−−√≥0x2≥0. But what does x2−−√x2 equal to?
Let's consider following examples: If x=5x=5 > x2−−√=25−−√=5=x=positivex2=25=5=x=positive; If x=−5x=−5 > x2−−√=25−−√=5=−x=positivex2=25=5=−x=positive."
My doubt is as follows
All we know that sqrt of a number can be positive or negative results both, how you are saying "square root function can not give negative result"? If you kindly answer this question it would be a great help for me. Looking forward to hear you from.




Re: Is ((x3)^2)^(1/2) = 3x? (1) x ≠ 3 (2) xx > 0
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