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How do you find the square root of 324?

Answer 1

Ethan Adkins

Factorize 324 and use root laws. See below

#324=2^2xx3^4#

#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#

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Answer 2

Kennedy Adams

#18#

#sqrt324#

#(1)#

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#

#(2)#

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

#324=2^2xx3^4#

this is left as an exercise for the student to verify

#:. sqrt324=sqrt(2^2xx3^4)#

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

#sqrt324=sqrt(2^2) xxsqrt(3^4)=2^1xx3^2#

#=2xx9=18#

as before

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.