How do you simplify #sqrt(45a^5)#?

1 Answer
mason m
Jan 22, 2016

#3a^2sqrt(5a)#

Explanation:

The square root will undo anything with a squared term. For example:

#sqrt18=sqrt(3^2xx2)=sqrt(3^2)xxsqrt2=3sqrt2#

Note how the square root and squared term in #sqrt(3^2)# cancelled to leave just #3#.

Similar logic can be applied to the current problem:

#sqrt(45a^5)=sqrt(3^2xx5xxa^4xxa)=sqrt(3^2)xxsqrt5xxsqrt((a^2)^2)xxsqrta#

#=3xxsqrt5xxa^2xxsqrta=3a^2sqrt(5a)#

Related questions
Impact of this question
3270 views around the world
You can reuse this answer
Creative Commons License