immune wrote:
I was wondering why we are not considering the negative roots of 4 in this case. For instance, sq root of 4 would be 2 and -2...same for the 4th root... Any rule / trick that I might be missing here?
Look forward to the answer.
Cheers!
Welcome to GMAT Club. Below might help to clear your doubts.
1. GMAT is dealing only with
Real Numbers: Integers, Fractions and Irrational Numbers.
2. Any nonnegative real number has a
unique non-negative square root called
the principal square root and unless otherwise specified,
the square root is generally taken to mean
the principal square root.
When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the
only accepted answer is the positive root.
That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, \(\sqrt{25}=+5\) and \(-\sqrt{25}=-5\).
Even roots have only non-negative value on the GMAT.Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
For more check Number Theory chapter of Math Book:
https://gmatclub.com/forum/math-number-theory-88376.htmlIn some data sufficiency questions, the answer becomes insufficient because the square root produces a plus and a minus value. I've been roasted many times for making this careless mistake. But in this question, I got it wrong because I considered -2 as a secondary answer in \(\sqrt{4}\)
Thank you.