When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, \(\sqrt{25}=+5\) and \(-\sqrt{25}=-5\). Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

Hope it helps.
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Is n > 6?

(1) \(\sqrt{n} > 2.5\) --> \(n>(2.5^2=6.25)\). Sufficient.

(2) \(n > \sqrt{37}\). Since \(\sqrt{37}> \sqrt{36}\), then \(n > \sqrt{37}>\sqrt{36}\) --> \(n>6\). Sufficient.

Answer: D.
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can Sqrt take a negative form . ?

Square roots are always positive.

If the problem said \(n^2 > 36\), then n could be > or < 6.

1.\(\sqrt{n}>2,5\) becomes \(n>(2,5)^2\), 2,5^2 (because 25*25=625) is 6,25 so n>6,25. Sufficient

2.\(n>\sqrt{37}\) because \(\sqrt{36}=6,\sqrt{37}>6\), we combine this equations in one: \(n>\sqrt{37}>6\) so n>6. Sufficient
IMO D

Hi,
Thanks for the response, but got one question.
How can you be sure that (square root 37) is only 6...why did not you consider (-6)..
when (square root 37) is considered as (-6) n>6 may not be possible...
so B option is not giving an answer with certainty..what do you say?

regards

In the GMAT \(\sqrt{25}=5\) and \(\sqrt{36}=6\), the square root of a number is its positive value.

Hi, even though it may seems like basic and stupid, but I just want to ask it for clearing my brain.
If in GMAT square root is always positive that why cant I take any given number, for eg in the 2nd statement in above equation and say since \(n>\sqrt{37}\) than \(n^2 >37\) and if I again do a Square root n>6 since I can ignore the -tive -6. since even square-root cannot have a negative value.
Can I do that? if no, can someone explain me why, and what stops me to do that? can anyone explain me with illustration or an eg?

Something like n^2 = 36 is different from n= square root 36. In the first case, n can have both positive and negative value because both value satisfy the equation. In the 2nd case, you are explicitly saying that n is positive square root of 36 which is +6. If you try to take the square root of a negative number than that square root takes you to the concept of imaginary numbers. GMAT is not concerned with it and hence you will never see something like n^2 = -36.

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Yes I am explicitly saying that because for \(\sqrt{36}\) as per Gmat -6 shouldn't be an option other wise if your are given statement like x= \(\sqrt{36}\) you will have to consider 2 roots +-6, whereas we say that even square root will only have positive number as a answer in Gmat, coz -6 is imaginary

- 6 is NOT imaginary, SQUARE ROOT (or any even root) of a negative integer is imaginary (imaginary numbers are out of scope for GMAT).

Guys, could you please point me to the instructions where we are asked to consider only positive roots for numbers?

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, \(\sqrt{25}=+5\) and \(-\sqrt{25}=-5\). Even roots have only non-negative value on the GMAT.
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Hi Bunuel,

My question showed stated one as "2.5" not "25'.

I didn't what the (2.5) ^2 was so I did 2^2 = 4 and (1/2)^2 = 1/4, therefore, less than 5.

How are we supposed to square something like 2.5?

2.5^2 = (5/2)^2 = 25/4. Or just square 25 and move decimal point two places to the left: 25^2 = 625, thus 2.5^2 = 6.25.
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Target question: Is n > 6?

Statement 1: √n > 2.5
Square both sides to get: n > (2.5)²
Evaluate to get: n > 6.25
If n > 6.25, then we can be CERTAIN that n > 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > √37
First recognize that √36 < √37
In other words, 6 < √37
Statement 2 tells us that √37 < n
So, we can COMBINE the inequalities to get 6 < √37 < n
From this, we can conclude that n > 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

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What if n lies between sqt36 and sqt37?

n cannot be between these numbers.

(2) says that \(n > \sqrt{37}\) and \(\sqrt{37}>\sqrt{36}\), so \(n > \sqrt{37}>\sqrt{36}\).
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Q) Is n>6?

1) root n> 2.5
n^2=2.5*2.5
= 6.25 (sufficeint)

2) n>root 37
use approx 36, the root of 36 will be 6, so n>6
(sufficient)
ANS D