5. Simplify

Sqrt(20x^3y^7)

Break the coefficient up into a product of primes, and spread

out all the variable factors.

Sqrt((2)(2)(5)xxxyyyyyyy)

Break the radical up around pairs of factors wherever possible.

 

Sqrt2^2Sqrt5Sqrtx^2Sqrtx(Sqrty^2)^3Sqrty

Two factors inside a radical is the same as one factor outside.

2(Sqrt5)x(Sqrtx)y^3(Sqrty)

Put all the factors outside the radical together in front of the

radical, and all of the factors which are still inside a radical under the

same radical.

2xy^3Sqrt(5xy)