If a^(1/2)=b, what is the value of integer b?

First of all, GMAT dose not have its own math.

Here (1) is sufficient because we want the value of b, and (1) directly gives it to us: b = |2| = 2. If we were asked to get the value of a, (1) still would have been sufficient. b = |2| = 2, so \(\sqrt{a}=2\), and a = 4 only, NOT 4 or -4 (you can square to get a = 4).

Next, 4 has two square roots 2 and -2 but \(\sqrt{}\) sign always means non-negative square root, so \(\sqrt{4}=2\) only.


\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.


The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).