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## Comment on

Equations with Square Roots## Thanks for very great

So if we get a question in GMAT that contains extraneous root, we take it as positive, am i correct?

## Extraneous roots aren't

Extraneous roots aren't necessarily negative. So, we always have to check for extraneous roots.

Consider this example: sqrt(13 - x) = 1 - x

Square both sides to get: 13 - x = (1 - x)^2

Expand: 13 - x = 1 - 2x + x^2

Rearrange: x^2 - x - 12 = 0

Factor: (x + 3)(x - 4) = 0

So, we have two possible solutions: x = -3 and x = 4

Now plug them back in to the original equation to check for EXTRANEOUS roots.

If x = -3, we get: sqrt[13 - (-3)] = 1 - (-3)

Simplify: sqrt(16) = 4

This WORKS, so one solution is x = -3

If x = 4, we get: sqrt(13 - 4) = 1 - 4

Simplify: sqrt(9) = -3

NO GOOD!

In this case, the solution with the NEGATIVE value was the GOOD solution, and the solution with the POSITIVE value was the EXTRANEOUS root.

## when (-1)^2 and (1)^2 both is

## Good question. Also a very

Good question. Also a very common question.

From the Official Guide:

"A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example, √9 denotes 3"

So, the square root NOTATION tells us to take the POSITIVE root.

As such, √1 = 1 (and only 1)

Also, -√1 = -1

## Hi Brent! Could you please

## Done!

Done!

See https://gmatclub.com/forum/if-4-x-1-2-x-2-then-x-could-be-equal-to-which...

## Hi Brent! At 1:58 you said a

## Hi Mohammad,

Hi Mohammad,

Every positive number has two square roots, however the square root NOTATION tells us to take the POSITIVE root.

So, for example, √81 = 9 (only)

From the OFFICIAL GUIDE FOR GMAT REVIEW:

"A square root of a number n is a number that, when squared, is equal to n. Every positive number n has two square roots, one positive and the other negative, but √n denotes the positive number whose square is n. For example, √9 denotes 3"

So, the square root NOTATION tells us to take the POSITIVE root.

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