yes brother. the reason being that the LHS has to be positive ( since we are taking square root). hence you can say that x-3>0 which means x>3

now you will get 2 values satisfying this equation. x= 1 and x= 6 we will consider only x= 6 because @ x=1 the right side becomes -ve.


Let me know if you need further explanation.

Hey, thanks for the quick reply..

Well, the square root of a number can be both positive & negative.

So, if we consider x=6, then the LHS becomes square root of 9 which is either +3 or -3, similarly for x=1, LHS becomes square root of 4, which can be either +2 or -2.

I am still confused...Please help!!

Yes square root can be both positive or negative. but for GMAT since we only talk about real numbers we consider positive. square root of a negative number becomes imaginary. Hence we dont consider.

bhai, I didn't consider square root of a negative number, rather, I am considering negative square root of a natural number...

well, the original question didn't provide options to choose from. May be, in the actual exam, I can choose out of the options provided. But, still, as far as I remember, I have seen some questions from OG where they consider, negative roots as well.

pankajks2010 wrote:Hi,

This question is from Manhattan flash cards.

Find the value of x: (x+3)^(1/2) = x-3



The OA is only 6 and not 1. will be great, if someone could help why 1 is not a possible answer.

I received a PM asking me to comment.

The MGMAT flash card reads as follows:
√(x+3) = x-3

The √ symbol means "positive root only".

Thus, if we solve by squaring both sides, we can consider only the positive root of √(x+3):
(√(x+3))² = (x-3)²
x+3 = x² - 6x + 9
x² - 7x + 6 = 0
(x-6)(x-1) = 0
x = 6, 1.

But x=1 results in the negative square root of √(x+3) and thus is not allowed:
√(1+3) = 1-3
√4 = -2.

Since √ means the positive root only, only x=6 is possible:
√(6+3) = 6-3
√9 = 3.
Thus, the only possible solution is x=6.

So remember what the different notations imply:
√16 = 4.
However, if x²=16, then x = ±4.

This is an important distinction to remember when taking the GMAT.

GMATGuruNY wrote:
So remember what the different notations imply:
√16 = 4.
However, if x²=16, then x = ±4.

This is an important distinction to remember when taking the GMAT.

Thank you so much Mitch!!

a useful link to practise this concept further:
https://www.beatthegmat.com/ds-question-t1515.html

even this one;
https://www.scorechase.com/gmat/content/ ... -half.html