How do you simplify #sqrt(45)#?

1 Answer
Rhys
Mar 3, 2018

#sqrt(45) = 3sqrt(5) #

Explanation:

We must use our knowledge of surds:

#sqrt(a*b*c) = sqrt(a)*sqrt(b)*sqrt(c) #

We know #45 = 3*3*5 #

#=> sqrt(45) = sqrt(3*3*5) = sqrt(3)*sqrt(3)*sqrt(5) #

We know #sqrt(a) * sqrt(a) = a#

#=> sqrt(3)*sqrt(3)*sqrt(5) = color(red)(3 *sqrt(5) #

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