How do you simplify #sqrt(75)# ?

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Answer 1 · 2016-09-11T07:26:57

#sqrt(75) = 5sqrt(3)#

First factorise #75#:

#75 = 3*5*5#

Next note that if #a, b >= 0# then:

#sqrt(ab) = sqrt(a)sqrt(b)#

Also if #a >= 0# then:

#sqrt(a^2) = a#

So we find:

#sqrt(75) = sqrt(5^2*3) = sqrt(5^2)*sqrt(3) = 5sqrt(3)#