How do you find the square root of 324?

May 9, 2018

Factorize 324 and use root laws. See below

Explanation:

$324 = {2}^{2} \times {3}^{4}$

sqrt324=sqrt(2^2·3^4)=sqrt(2^2)·sqrt(3^2·3^2)=sqrt(2^2)·sqrt(3^2)·sqrt(3^2)=2·3·3=18

May 9, 2018

$18$

Explanation:

$\sqrt{324}$

$\left(1\right)$

I used to make my students memorise all the squares, and the corresponding square roots, up to 20. So if you did this you would be able to write the answer straight down as being $18$

$\left(2\right)$

#If the number is outside the students range then using prime factors is a a good way to go

$324 = {2}^{2} \times {3}^{4}$

this is left as an exercise for the student to verify

$\therefore \sqrt{324} = \sqrt{{2}^{2} \times {3}^{4}}$

to square root numbers with powers simply half the powers of each number

$\sqrt{324} = \sqrt{{2}^{2}} \times \sqrt{{3}^{4}} = {2}^{1} \times {3}^{2}$

$= 2 \times 9 = 18$

as before