Question

Find the square root of 324 by prime factorization method. Show full answer.

Answer 1

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Answer 2

The square root of 324 = 18

Given :

The number 324

To find :

Find the square root of 324 by prime factorization method.

Solution :

Step 1 of 3 :

Write down the given number

The given number is 324

Step 2 of 3 :

Prime factorise the number

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:324 \:\:}}}\\ {\underline{\sf{2}}}&\underline{\sf{\:\:162 \:\:}} \\ {\underline{\sf{3}}}&\underline{\sf{\:\:81 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:27\:\:}}\\\underline{\sf{3}}&\underline{\sf{\:\:9\:\:}} \\ {\underline{\sf{3}}}&\underline{\sf{\:\:3\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

324 = 2 × 2 × 3 × 3 × 3 × 3

∴ 324 = 2² × 3² × 3²

Step 3 of 3 :

Find the square root of 324

$\displaystyle \sf{ \sqrt{324} }$

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

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

$\displaystyle \sf{ = 18 }$

Hence square root of 324 = 18

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