5- root of y to the power of 2

5 - root(y^2) = -3
5+3 = root(y^2)
8 = root(y^2)
64 = y^2
y = +8 or -8

Thanks Ashley. One quick question. Can we write the equation like

5-y = -3 by canceling square root with square?

vidhya16 wrote: One quick question. Can we write the equation like

5-y = -3 by canceling square root with square?

Hi,
Square root of a number is always the positive root.
So, sqrt(y^2) = |y|
Example: sqrt((-3)^2) = |-3| = 3
sqrt(3^2) = |3| = 3
So you can write 5-sqrt(y^2) as 5 - |y|
Now solve, 5 - |y| = -3 =>|y| = 8. So, y = 8 or -8.

vidhya16 wrote:5 -√y² = -3 .Whats the value of y?

Ta

√y² = |y|
so 5 -√y² = -3 -> 5 -|y| = -3
case 1: if y>0, 5-y = -3 -> y= 8
case 2: if y<0, 5-(-y) = -3 -> y=-8

so y = 8 or -8.

vidhya16 wrote:Thanks Ashley. One quick question. Can we write the equation like

5-y = -3 by canceling square root with square?

since √y² is positive so you can't write √y² = y as we don't know whether y is positive or not but we certainly know that √y² is positive.

so we can write √y² = |y|
hence √y² = y if y>0.
and √y² = -y if y<0.

I hope it is clear ..if not try some numerical values ..

Just want to confirm the replies given above -- it's exactly right that you CAN'T simplify root(y^2) to y safely, for precisely the reason explained: if y is negative, root(y^2) will NOT equal y but rather the opposite of y.

I think this problem is a nice illustrator of a good GMAT lesson: if it looks weird, there's probably a reason it needs to. If I came to this problem on the test, I might be inclined to react initially with a sentiment along the lines of "That's silly... why would they write root(y^2) rather than just simply y? That seems indirect, like saying 'I'm not not a girl.'" But then hopefully I'd ponder that some more... like really, why WOULD they write it like that? I'd try to think of a reason. And then I'd realize that it's because "root(y^2)" actually has a different meaning from "y"... and that whether or not you realize that is really the primary thing the problem is testing.

Ashley@VeritasPrep wrote:Just want to confirm the replies given above -- it's exactly right that you CAN'T simplify root(y^2) to y safely, for precisely the reason explained: if y is negative, root(y^2) will NOT equal y but rather the opposite of y.

Thanks Ashley for confirming my post...
'I'm not not a girl... hehhehehhe what an example, but what does that exactly mean...

@Frankenstein .. For more simplification I discussed it in my latest post "Is √x² = x or -x or none" on my blog https://mba.webmaggu.com/is-%E2%88%9Ax%C ... x-or-none/ . so check it out.. Hope it would help you a lot, as this is a common confusion among a lots of students...

I also had the same doubt with a similar problem. √ (-3)^2 < 0, true or false?

√9 = +3 or -3 so..?

The OA is false as √9 = 3 according to them. I also saw before that when it's √x then it's +x that's wanted. When it's x^2 and you're square rooting then it could be + or - x

MBA.Aspirant wrote:I also had the same doubt with a similar problem. √ (-3)^2 < 0, true or false?

√9 = +3 or -3 so..?

The OA is false as √9 = 3 according to them. I also saw before that when it's √x then it's +x that's wanted. When it's x^2 and you're square rooting then it could be + or - x

Yes, so technical the √x means "the principal square root of x," where the word principal means "nonnegative." So the function y = √x is actually only defined over the nonnegative real numbers (that is, both in terms of its domain and in terms of its range). It looks like this -- the graph does not exist in any other quadrants:



In contrast, when you just have y = x^2, or x^2 = 16, or whatever, we don't have that √ symbol popping up and meaning "the principal square root." So x can take on any value that will satisfy the equation, and since squaring any negative number always yields the same thing as does squaring its positive counterpart, all equations of this form will have two possible solutions. (That's why we wind up with a parabola in two quadrants instead of just one when we graph y = x^2.)