Question

Find the square root of 324.

Answer 1

Hint: In this question we have to find the square root of the given number. Square of any number A means ${\left(A\right)}^{{\displaystyle \frac{1}{2}}}$. Use this concept along with basic factorization techniques of the given number to get the answer.

Complete step-by-step answer:
Given number is 324.

Now we have to find out the square root of this number.

i.e. $\sqrt{324}$ .

This is also written as ${\left(324\right)}^{{\displaystyle \frac{1}{2}}}$……… (1)

So first factorize the given number,

$\Rightarrow 324=2\times 2\times 3\times 3\times 3\times 3=\left(2^2\right)\left(3^4\right)$

So substitute this value in equation (1) we have,

$\Rightarrow {\left(324\right)}^{{\displaystyle \frac{1}{2}}}={\left(\left(2^2\right)\left(3^4\right)\right)}^{{\displaystyle \frac{1}{2}}}=\left(2^{2\times {\displaystyle \frac{1}{2}}}\right)\left(3^{4\times {\displaystyle \frac{1}{2}}}\right)=2\left(3^2\right)=2\left(9\right)=18$.

So the required square root of 324 is 18.

Hence option (A) is correct.

Note: Whenever we face such types of problems the key concept is simply to have the basic understanding of the square root that is the number raised to the power half. Factorization is the method of obtaining all the factors of the given number. Use these concepts to get on the right track for solving problems of this kind.