marcovg4 wrote:
According to GMAT square root of a number is always positive, so SqRt of 25 is ONLY 5, SqRt of 81 is ONLY 9.
Then, why in this case SqRt of 64 yields +-8?
You're right, but the question here is different.
We are not applying the root to 64 only, but to the left term as well. Consider the following case:
If I say b=\(\sqrt{64}\) then \(b=8\).
But if I say \(b^2=64\) (for example) then b can have two values: 8 and -8. Here the root is applyed to both terms \(\sqrt{b^2}=\sqrt{64}\) and the solutions are +-8 => \((-8)^2=64\) and \(8^2=64\).
Whenever you have an expression in the form \(\sqrt{x^2}\) you translate it into \(|x|\). So from the upper example you get \(|b|=|8|\) or b=+-8.
So, with the same method, from \((b+4)^2 = 64\) you obtain \(|b+4| = |8|\) => b+4=+-8 or if you prefer +-(b+4)=8.
Hope it's clear