aces021 wrote:4x^2=y^2-3^2

Is it possible to take the square root of the right side?

Since they are being subtracted our only option is to put it in this form (y-3)(y+3). We are not allowed to do √y^2-3^2 = y-3. Is this correct?

You are right.
We cannot take the expression y² - 3² and rewrite it as (some expression)(the same expression). Therefore, we can't find a "nice" square root of y² - 3²
The best we can do is rewrite it as (y + 3)(y - 3)

Also note that we can easily confirm whether or not √(y² - 3²) = (y - 3)
Aside: Since √25 = 5, we know that (5)(5) = 25
Likewise, since √49 = 7, we know that (7)(7) = 49
So, IF √(y² - 3²) = (y - 3), then it must be true that (y - 3)(y - 3) = y² - 3²
HOWEVER, (y - 3)(y - 3) = y² - 6y + 9
So, √(y² - 3²) ≠ (y - 3)

Cheers,
Brent

We can also confirm whether or not √(y² - 3²) = (y - 3) by plugging in some value of y
Let's plug in y = 4
We get √(4² - 3²) = (4 - 3)
Evaluate to get: √7 = 1 NOPE
So, √(y² - 3²) ≠ (y - 3)

Cheers,
Brent

Hi aces021,

Is this equation part of a larger GMAT question or are you just interested in the algebra?

Since we cannot take the square root of both sides, that "math move" would not be part of the solution to whatever question this was included in.

GMAT assassins aren't born, they're made,
Rich