Question

Find the cube root of \[{\text{8000}}\].

Answer 1

Hint: Here, first we have to do prime factorisation of \[{\text{8000}}\], then make the pair of three same numbers.

Complete step-by-step answer:
Cube root of \[{\text{8000}}\].
\[{\text{8000}}\] can also be written as ,
$8000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 2 \times 2 \times 2$
On taking cube root of both sides we get,
$\sqrt[3]{{8000}} = \sqrt[3]{{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5}} = {2^{2 \times 3 \times \left( {\dfrac{1}{3}} \right)}} \times {5^{\left( {3 \times \dfrac{1}{3}} \right)}} = 2 \times 2 \times 5 = 20$
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.