# $

{\text{Q}}{\text{.Find out the cube root of 216}}{\text{.}} \\

{\text{A}}{\text{. 8}} \\

{\text{B}}{\text{. 4}} \\

{\text{C}}{\text{. 9}} \\

{\text{D}}{\text{. 6}} \\

\\

$

Answer

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369.6k+ views

$

{\text{In mathematics a cube root of a number }}x\,{\text{ is number }}y\,{\text{such that }}{y^3} = x\,\,\,\,....\left( 1 \right) \\

{\text{now finding the cube root of the number by prime factorization}}{\text{.}} \\

{\text{from the equation one }} \\

{y^3} = 216 \\

y = \sqrt[3]{{216}} \\

{\text{prime factors of are }} \\

{\text{216 = 2}} \times {\text{2}} \times {\text{2}} \times {\text{3}} \times {\text{3}} \times {\text{3}} \\

{\text{now assume three time repeating digits as one}}{\text{.}} \\

{\text{as here by assuming each three as one we will get 2and 3}}{\text{.}} \\

{\text{now we should multiply these numbers}}{\text{.}} \\

{\text{2}} \times {\text{3 = 6 }} \\

\sqrt[3]{{216}} = 6 \\

{\text{which is the cube root of 216 as mentioned}}{\text{.}} \\

{\text{NOTE: whenever you come across this kind of question find out the prime factors of the given number}} \\

{\text{ and always assume the three time repeating digit as one and multiply them to get the cube root }} \\

{\text{ of the number }} \\

$

{\text{In mathematics a cube root of a number }}x\,{\text{ is number }}y\,{\text{such that }}{y^3} = x\,\,\,\,....\left( 1 \right) \\

{\text{now finding the cube root of the number by prime factorization}}{\text{.}} \\

{\text{from the equation one }} \\

{y^3} = 216 \\

y = \sqrt[3]{{216}} \\

{\text{prime factors of are }} \\

{\text{216 = 2}} \times {\text{2}} \times {\text{2}} \times {\text{3}} \times {\text{3}} \times {\text{3}} \\

{\text{now assume three time repeating digits as one}}{\text{.}} \\

{\text{as here by assuming each three as one we will get 2and 3}}{\text{.}} \\

{\text{now we should multiply these numbers}}{\text{.}} \\

{\text{2}} \times {\text{3 = 6 }} \\

\sqrt[3]{{216}} = 6 \\

{\text{which is the cube root of 216 as mentioned}}{\text{.}} \\

{\text{NOTE: whenever you come across this kind of question find out the prime factors of the given number}} \\

{\text{ and always assume the three time repeating digit as one and multiply them to get the cube root }} \\

{\text{ of the number }} \\

$

Last updated date: 28th Sep 2023

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