How do you simplify #sqrt(972)#?

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Answer 1 · 2016-04-24T21:17:29

#18sqrt(3)#

972 ends in 2, therefore is divisible by 2:

#972/2=486#

divisible by 2 again:

#486/2=243#

The sum of digits is multiple of 3, so 243 it is divisble by 3:

#243/3=81#

#81=9xx9=3^4#

so #972=2^2xx3^5#

#sqrt(972)=sqrt(2^2xx3^5)=sqrt(2^2xx3^4xx3)=2xx3^2sqrt(3)=18sqrt(3)#