Question

# Find the cube root of ${\text{8000}}$.

Hint: Here, first we have to do prime factorisation of ${\text{8000}}$, then make the pair of three same numbers.
Cube root of ${\text{8000}}$.
${\text{8000}}$ can also be written as ,
$8000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2$
$\sqrt[3]{{8000}} = \sqrt[3]{{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5}} = {2^{2 \times 3 \times \left( {\dfrac{1}{3}} \right)}} \times {5^{\left( {3 \times \dfrac{1}{3}} \right)}} = 2 \times 2 \times 5 = 20$
Hence the cube root of ${\text{8000}}$ is ${\text{20}}$.
Note: In these types of questions we must know that in mathematics, a cube root of number ${\text{x}}$ is a number ${\text{y}}$ such that the cube of y is equal to x . All non zero numbers have only one real root . Doing prime factorisation and making the pair of three same numbers will make the problem more easy to solve.