Question

find the cube root of 166375

Answer 1

$\huge\mathcal{Heya}$

$\mathsf\red{By \ prime \ factorisation \ method}$
$<b><i>$
In this method, we break down the number into its simplest factors.


If we want to find out square root, then we make the pair of that number, using its factors.


If we want to find out cube root, then we make the triplet of that number, using its factors.

Now,

166375 can be break down into :-

= 5 × 5 × 5 × 11 × 11 × 11

Cube root of 166375 :-

$= \sqrt[3]{166375} \\ \\ = \sqrt[3]{5 \times 5 \times 5 \times 11 \times 11 \times 11} \\ \\ = \sqrt[3]{ {5}^{3} \times {11}^{3} } \\ \\ = {( {5}^{3} \times {11}^{3}) }^{ \frac{1}{3} } \\ \\ = {( {5}^{3}) }^{ \frac{1}{3} } \times { ({11}^{3}) }^{ \frac{1}{3} } \\ \\ = {5}^{3 \times \frac{1}{3} } \times {11}^{3 \times \frac{1}{3} } \\ \\ = 5 \times 11 \\ \\ 55$

•°•

55 is the cube root of 166375.

$\huge\mathbb{Hope \ this \ helps.}$

Answer 2

Hii !!

166375

Prime factorisation of 166375 = 5 × 5 × 5 × 11 × 11 × 11

Therefore,

Cube root of 166375 = ³√5•5•5•11•11•11


=> ³√5³•11³



=> (5³•11³)⅓



=> 5³×⅓ × 11³× ⅓



=> 5¹ × 11¹ = 5 × 11



=> 55

Hence,

Cube root of 166375 = 55.