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

1 Answer
May 13, 2015

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)).