Question

Find the cube root of 216 by prime factorisation

Answer 1

$\sqrt[3]{216} = \sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3}$

=2×3

=6

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Answer 2

The cube root of 216 = 6

Given :

The number 216

To find :

The cube root of 216 by prime factorisation

Solution :

Step 1 of 3 :

Write down the given number

Here the given number is 216

Step 2 of 3 :

Prime factorise the number

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:216 \:\:}}}\\ {\underline{\sf{2}}}&\underline{\sf{\:\:108 \:\:}} \\ {\underline{\sf{2}}}&\underline{\sf{\:\:54 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:27\:\:}}\\\underline{\sf{3}}&\underline{\sf{\:\:9\:\:}} \\ {\underline{\sf{3}}}&\underline{\sf{\:\:3\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

Thus we get

$\displaystyle \sf 216$

$\displaystyle \sf = 2 \times 2 \times 2 \times 3 \times 3 \times 3$

$\displaystyle \sf = {2}^{3} \times {3}^{3}$

Step 3 of 3 :

Find cube root of 216

Hence the cube root of 216

$\displaystyle \sf{ = \sqrt[3]{216} }$

$\displaystyle \sf{ = \sqrt[3]{ {2}^{3} \times {3}^{3} } }$

$\displaystyle \sf{ = 2 \times 3 }$

$\displaystyle \sf{ = 6 }$

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