Name: Introduction to Cube roots of numbers
Uploaded: 2019-07-19
Duration: 15 min 49 s
Description: In this video, we will discuss the basics and methods to find out the cube roots of numbers. This video will be helpful for all the competitive examinations....

Question

Find the cube root of $22 \frac{161}{216}$

Accepted Answer

Given to find cube root of $22 \frac{161}{216}$

We find cube root of mixed fraction by converting it into simple fraction.

We know that,

If $\frac{a}{b}$ is a rational number, where $' a' a n d' b'$ are co-prime and perfect cubes, and $b \neq 0$ then $\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}$

$\Rightarrow 22 \frac{161}{216} = \frac{4913}{216}$

$\Rightarrow \sqrt[3]{22 \frac{161}{216}} = \sqrt[3]{\frac{4913}{216}} = \frac{\sqrt[3]{4913}}{\sqrt[3]{216}}$

$= \frac{\sqrt[3]{17 \times 17 \times 17}}{\sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3}}$

$= \frac{17}{2 \times 3}$

$∴ \sqrt[3]{22 \frac{161}{216}} = \frac{17}{6} = 2 \frac{5}{6}$

Hence, cube root of $22 \frac{161}{216} = 2 \frac{5}{6}$ .

Find the cube root of $22 \frac{161}{216}$

Important Questions on Cube Root

Learn and Prepare for any exam you want !

Find the cube root of 22 161 216

Important Questions on Cube Root

Learn and Prepare for any exam you want !

Find the cube root of $22 \frac{161}{216}$