Question

how to find cube root of a decimal place number like 1157.625

Answer 1

Answer:

$\displaystyle\mathsf{\sqrt[3]{1157.625}=10.5}$

Step-by-step explanation:

$\textsf{Cube root of the given number is found by factorization method}$

$\displaystyle\mathsf{\sqrt[3]{1157.625}}$

$\displaystyle\mathsf{=\sqrt[3]{\frac{1157625}{1000}}}$

$\displaystyle\mathsf{=\sqrt[3]{\frac{7*7*7*5*5*5*3*3*3}{10*10*10}}}$

$\displaystyle\mathsf{=\frac{7*5*3}{10}}$

$\displaystyle\mathsf{=\frac{105}{10}}$

$\displaystyle\mathsf{=10.5}$

$\implies\boxed{\displaystyle\mathsf{\sqrt[3]{1157.625}=10.5}}$