SHRAVYA007
Gprabhumir, The radical sign does not imply that the root will be positive only. When dealing with square roots, for instance, it is common to consider both positive and negative roots. The symbol ’√’ itself represents the principal (positive) square root, but to account for both possibilities, we use the ’±’ symbol before the radical sign. This signifies both the positive and negative square roots of a number.
GprabhumirSHRAVYA007That's not right.
Mathematically, \(\sqrt{...}\) 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) = √xNotice 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:
√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 =-√9 =-3 or x = √9 = 3.
Hope it helps.
Check this forum link to see the formulae properly:
https://gmatclub.com/forum/quant-chat-g ... l#p3311523