Question

Find the cube root of 125.

Answer 1

Hint: 125 is a perfect cube. A perfect cube is a number which is the multiple of 3 same numbers for example 1, 8, 27, 64 etc

Here we have to find the cube root of 125.
So let $y = 125$
Now the cube root of 125 means we have to find ${\left( {125} \right)^{\frac{1}{3}}}$. So taking cube root on both sides of the above equation, we get
${\left( y \right)^{\frac{1}{3}}} = {\left( {125} \right)^{\frac{1}{3}}}$
$ \Rightarrow {\left( y \right)^{\frac{1}{3}}} = {\left( {{5^3}} \right)^{\frac{1}{3}}}$ as we know that $125 = {5^3}$
$ \Rightarrow {\left( y \right)^{\frac{1}{3}}} = 5$ which is our required answer

Note - Whenever we come across such questions simply put the value whose cube root is to be found equal to some variable and then take the cube root on both sides, this eventually helps in cancellation of powers and getting the solution.