How do you simplify #sqrt(a^11)+sqrt(a^5)#?

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Answer 1 · 2015-05-13T16:48:24

By factoring:

First: #sqrt(a^11) = sqrt(a*a*a*a*a*a*a*a*a*a*a) = sqrt(a^2*a^2*a^2*a^2*a^2*a) = a*a*a*a*a*sqrt(a) = a^5sqrt(a)#

Second: #sqrt(a^5) = sqrt(a*a*a*a*a) = sqrt(a^2*a^2*a) = a^2*sqrt(a)#

Now, summing again:

#a^5*sqrt(a) + a^2*sqrt(a)#

#a^2*a^3*sqrt(a) + a^2*sqrt(a)#

=

#(a^3 + 1)(a^2*sqrt(a))#

My final answer would be: #(a^3+1)(a^(5/2))#.