How do you simplify #sqrt324#?

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Answer 1 · 2016-02-21T21:39:24

#sqrt(324)=18#

#color(brown)("Have a look at how I used the Factor Tree to help arrive at an answer")##color(brown)("without using a calculator.")#

Lets see if we can split 324 into a product of squared primes:

Consider the Factor Tree:

#color(blue)("If the sum of the digits is divisible by 3 then the whole is divisible by 3")#

Tony B

From this we have #2^2xx3^2xx3^2" " =" " 4xx9^2" "=" "324#

So write #" "sqrt(324)" as " sqrt(2^2xx3^2xx3^2)#

Giving:#" " 2xx3xx3" "=" "18 #