tejal777 wrote:
The value of cube root of (-89) is..?
Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined
...................
Is'nt the root of any negative number undefined?
Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): \(\sqrt[{even}]{negative}=undefined\), for example \(\sqrt{-25}=undefined\).
Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
The above question is quite tricky:
\(\sqrt[3]{-89}\) is
more than -5 (as \(-5^3=-125\)) but
less than -4 (as \(-4^3=-64\)) --> \(-5<x<-4\), (actually it's \(\approx{-4.5}\)). So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10).
Answer: A.
i did this quesiton wrong cuz remember your words that \(\sqrt{-25}=undefined\).
cube root means that it has to be a negative number after you took out. Then it should be something \sqrt{negative X} therefore should be undefined? where am i missing?