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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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26 Jun 2016, 00:36
\(\sqrt{x^2}=(x)\) because x > 0 \(\sqrt{y^2}=y\) because y > 0 \(\sqrt{x^2*y^2}= \sqrt{x^2} * \sqrt{y^2} = (x)y\)
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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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Updated on: 15 Aug 2016, 07:06
nehamodak wrote: What is \(\sqrt{x^2*y^2}\) if x < 0 and y > 0?
(A) –xy (B) xy (C) –xy (D) yx (E) No solution ANSWER IS A take x as 2 and y as 2 \(\sqrt{2^2*2^2}\) \(\sqrt{4*4}\) \(\sqrt{16}\) = 4 Now see what option gives you 4 x*y= 2*2=4 WRONG (x)*y = (2)*2 = 2*2 = 4 CORRECT
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Originally posted by LogicGuru1 on 24 Jul 2016, 23:56.
Last edited by LogicGuru1 on 15 Aug 2016, 07:06, edited 1 time in total.



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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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15 Aug 2016, 04:24
What's the difference between A and C?
Both will give us the same answer right?
A =  (of a positive xy) B =  (of a positive xy)



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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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16 Aug 2016, 01:42
ameyaprabhu wrote: What's the difference between A and C?
Both will give us the same answer right?
A =  (of a positive xy) B =  (of a positive xy) You are given that x < 0 (say x is 2) and y > 0 (say y is 5). So xy will be 2*5 = 10. Hence xy will actually be a negative number. Option (A) =  xy =  (10) = 10 (a positive number) Option (C) =  xy =  10 = 10 (a negative number)
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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16 Aug 2016, 03:15
got it. Thanks [quote="VeritasPrepKarishma"][quote="ameyaprabhu"]What's the difference between A and C?



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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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10 Sep 2016, 07:54
But isn't saying that x = x contradictory?.. You are saying that "something always positive equals a negative umber"
How can this be?
Or is this something like x =  (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative > negative X you get a positive X ?
The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number



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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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10 Sep 2016, 09:35
iliavko wrote: But isn't saying that x = x contradictory?.. You are saying that "something always positive equals a negative umber"
How can this be?
Or is this something like x =  (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative > negative X you get a positive X ?
The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number x = x implies what I have highlighted above.
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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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10 Sep 2016, 12:29
iliavko wrote: But isn't saying that x = x contradictory?.. You are saying that "something always positive equals a negative umber"
How can this be?
Or is this something like x =  (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative > negative X you get a positive X ?
The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number
x actually behaves differently for values greater than 0 and less than 0. In other words x has two cases CASE 1) x>0; for x >0 x = x For example 4= 4 Case 2) x<0; for x<0 x= x For example 4=  of 4 or (4)= 4 so to generalise x = (x); Now since x is a "variable" it is hiding a "Negative Polarity" inside itself in this case. YOU HAVE TO BE ABSOLUTELY CLEAR ABOUT IT. A VARIABLE CAN LOOK POSITIVE BUT IT MAY CARRY A HIDDEN POLARITY . For example x can be 9 but just looking at x you cannot quickly relate to 9. You will automatically see x as positive. BUT REMEMBER X IS A VARIABLE THAT CAN HAVE ANY POLARITY AND VALUE. THAT IS WHY SO MANY PEOPLE ARE GETTING CONFUSED IN THIS QUESTION. It is useless to rote or memorize the formula that x= x until and unless how it works in case of x>0 and x<0 Again to revise IF x>0 then x= x {plain and simple to remember} If x<0 then x=x {You need to understand the concept of hidden polarity inside a variable}. In this case particular example x will ultimately be a positive numerical value but if the question does not involve substitution of numerical values to x and x then you have to be solve the question very carefuly. Hope its clear to all now .
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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19 Apr 2017, 21:45
VeritasPrepKarishma, I don't understand your explanation: \(\sqrt{(x^2*y^2)}\) = x*y > I understand this part, but how do you then go here: "Now, if x < 0, x=−x" Let me rephrase:  if I told you that I know x=2, when you take 2, you get 2.  if, on the other hand, I told you that the value of x changed, and is now 25, then when you take 25, you get 25. * The point here being: the absolute value will give you the positive value of whatever is inside the brackets, regardless of what sign the content inside the bracket isSo I'm having a hard time rationalizing this: x=−x. How can the absolute value of a variable ever be negative?



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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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20 Apr 2017, 00:30
LakerFan24 wrote: VeritasPrepKarishma, I don't understand your explanation: \(\sqrt{(x^2*y^2)}\) = x*y > I understand this part, but how do you then go here: "Now, if x < 0, x=−x" Let me rephrase:  if I told you that I know x=2, when you take 2, you get 2.  if, on the other hand, I told you that the value of x changed, and is now 25, then when you take 25, you get 25. * The point here being: the absolute value will give you the positive value of whatever is inside the brackets, regardless of what sign the content inside the bracket isSo I'm having a hard time rationalizing this: x=−x. How can the absolute value of a variable ever be negative? What makes you say that x is a negative quantity? Note that the absolute value is x when x itself is negative. So x itself will have a negative sign and the two negatives will cancel off each other to give you a positive value. x is a way of expressing a positive quantity when x itself is negative. Does this make sense?
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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20 Apr 2017, 19:41
VeritasPrepKarishma wrote: LakerFan24 wrote: VeritasPrepKarishma, I don't understand your explanation: \(\sqrt{(x^2*y^2)}\) = x*y > I understand this part, but how do you then go here: "Now, if x < 0, x=−x" Let me rephrase:  if I told you that I know x=2, when you take 2, you get 2.  if, on the other hand, I told you that the value of x changed, and is now 25, then when you take 25, you get 25. * The point here being: the absolute value will give you the positive value of whatever is inside the brackets, regardless of what sign the content inside the bracket isSo I'm having a hard time rationalizing this: x=−x. How can the absolute value of a variable ever be negative? What makes you say that x is a negative quantity? Note that the absolute value is x when x itself is negative. So x itself will have a negative sign and the two negatives will cancel off each other to give you a positive value. x is a way of expressing a positive quantity when x itself is negative. Does this make sense? Let me see if I understand this correctly: x is always positive, and since we know that x is a negative number, in order to express a positive quantity, we need to add a negative to "cancel out" the negatives to make positive? This way, x = (negative value,x). If I were to substitute values for x (let's say, 2), then: 2 = (2)



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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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06 Jul 2017, 21:16
VeritasPrepKarishma wrote: nehamodak wrote: What is \sqrt{x^2*y^2} if x < 0 and y > 0? (A) –xy (B) xy (C) –xy (D) yx (E) No solution
Please explain how do we solve this Note that \(\sqrt{x^2} = x\). It is not x, it is x. When we talk about square root, it implies the principal square root i.e. just the positive square root. \(\sqrt{x^2*y^2} = x*y\) Now, if x < 0, \(x = x\) If y > 0, \(y = y\) Hence, \(x*y = x*y\) Answer (A) \(\sqrt{x^2} = x\) ^ in the above equation, if the X value is not specified, can you know for certain whether X is positive or negative? i.e.  the only way we know X is negative is because the stem tells us x<0. Without this information, are we unable to determine the sign of X?



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What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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06 Jul 2017, 21:19
LogicGuru1 wrote: iliavko wrote: But isn't saying that x = x contradictory?.. You are saying that "something always positive equals a negative umber"
How can this be?
Or is this something like x =  (X) , so "if X is negative then modulus is (obviously) positive and if you plug a negative X into a negative > negative X you get a positive X ?
The way the choice A is written, is misleading imo. It looks as you are saying that a modulus is somehow equivalent to a negative number
x actually behaves differently for values greater than 0 and less than 0. In other words x has two cases CASE 1) x>0; for x >0 x = x For example 4= 4 Case 2) x<0; for x<0 x= x For example 4=  of 4 or (4)= 4 so to generalise x = (x); Now since x is a "variable" it is hiding a "Negative Polarity" inside itself in this case. YOU HAVE TO BE ABSOLUTELY CLEAR ABOUT IT. A VARIABLE CAN LOOK POSITIVE BUT IT MAY CARRY A HIDDEN POLARITY . For example x can be 9 but just looking at x you cannot quickly relate to 9. You will automatically see x as positive. BUT REMEMBER X IS A VARIABLE THAT CAN HAVE ANY POLARITY AND VALUE. THAT IS WHY SO MANY PEOPLE ARE GETTING CONFUSED IN THIS QUESTION. It is useless to rote or memorize the formula that x= x until and unless how it works in case of x>0 and x<0 Again to revise IF x>0 then x= x {plain and simple to remember} If x<0 then x=x {You need to understand the concept of hidden polarity inside a variable}. In this case particular example x will ultimately be a positive numerical value but if the question does not involve substitution of numerical values to x and x then you have to be solve the question very carefuly. Hope its clear to all now . This helps and I just want to clarify that without the added information that x<0, there would be no way of determining whether X is positive or negative? Correct?



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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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06 Jul 2017, 23:42
ak1802 wrote: This helps and I just want to clarify that without the added information that x<0, there would be no way of determining whether X is positive or negative? Correct?
Hi ak1802 , Yes, that's true. We cannot find the nature of x unless we are given such condition.
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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27 Jul 2017, 16:50
VeritasPrepKarishmaam i correct in saying that \(\sqrt{x^{2}}\) is NOT the same as writing \(\sqrt{(x^{2})}\), so is this the reason here that \(\sqrt{x^{2}}\) = (x)? is this what the problem is testing? because otherwise, i cannot understand how an absolute value is negative  an absolute value can never be negative, because it is the measure of how far away numbers are on a number line



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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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27 Jul 2017, 21:04
LakerFan24 wrote: VeritasPrepKarishmaam i correct in saying that \(\sqrt{x^{2}}\) is NOT the same as writing \(\sqrt{(x^{2})}\), so is this the reason here that \(\sqrt{x^{2}}\) = (x)? is this what the problem is testing? because otherwise, i cannot understand how an absolute value is negative  an absolute value can never be negative, because it is the measure of how far away numbers are on a number line \(\sqrt{x^{2}}\) is the same as \(\sqrt{(x^{2})}\). \(\sqrt{x^{2}}=x\). We are given that x is negative. When x < 0, we know that x = x, so \(\sqrt{x^{2}}=x=x\). Notice that since x is negative, x = negative = positive, thus both the square root and the absolute value return positive result.
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Re: What is (x^2y^2)^1/2 if x < 0 and y > 0 ?
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27 Jul 2017, 21:17
LakerFan24 wrote: VeritasPrepKarishmaam i correct in saying that \(\sqrt{x^{2}}\) is NOT the same as writing \(\sqrt{(x^{2})}\), so is this the reason here that \(\sqrt{x^{2}}\) = (x)? is this what the problem is testing? because otherwise, i cannot understand how an absolute value is negative  an absolute value can never be negative, because it is the measure of how far away numbers are on a number line In addition to what Bunuel said above, let me also add a line on how I explain this in words: You are right. An absolute value can never be negative. So x will never be negative. But it can be equal to x. When? When x itself is negative. Note that a variable x CAN stand for a negative value too. So if x itself is negative, x becomes POSITIVE. And that is the case in which x is equal to x (which is positive).
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