Square root (negative or positive)

[samcr22]

Folks

I read this somewhere:

When you see a square root that the GMAT puts there, you only take the positive root. But when you decide to unsquare an equation by taking the square root of both sides, you MUST consider both possibilities (postive and negative)
Sample eq (x-1)squared = 625

I don't understand why this is the case and feel that in both situations, you should consider -ve and +ve results

Thanks!

[mkurteev123]

if i got you problem right, it looks like
(x-1)^2=625=25^2 ,x^2-y^2=(x-y)(x+y)
(x-1)^2-25^2=0
(x-1-25)(x-1+25)=0
x=26. x=-24

[gregoryssmith]

I always viewed it as being an unknown vs. a known.

When you take the square root of something then you are told the number that you are operating on. Say √4 is definitely 4 which has the root of 2. On the other hand, x^2 = 4 can mean 2 or -2 for x because the x part is unknown and could be either.

I hope that helps!

[jnelson0612]

I always viewed it as being an unknown vs. a known.

When you take the square root of something then you are told the number that you are operating on. Say √4 is definitely 4 which has the root of 2. On the other hand, x^2 = 4 can mean 2 or -2 for x because the x part is unknown and could be either.

I hope that helps!

Hi samcr,
gregoryssmith has given a good explanation here. The most important thing to remember is the rule:
a) The square root of a number, say 9, is its positive root only. In this case it is 3.
b) However, if I have x^2 = 9, I must consider that either -3 or 3 squared equals 9. So x could be 3 or -3.

This is a good rule to put on a flash card if you aren't 100% solid with it.

Best wishes,