Simplify square root of 512m^3

Problem

√(,512*m3)

Solution

1. Factor the radicand into perfect squares and remaining factors.

512=256⋅2

m3=m2⋅m

2. Rewrite the square root by grouping the perfect square terms together.

√(,256⋅m2⋅2⋅m)

3. Apply the product property of radicals √(,a⋅b)=√(,a)⋅√(,b) to separate the perfect squares.

√(,256)⋅√(,m2)⋅√(,2*m)

4. Simplify the square roots of the perfect squares.

16⋅m⋅√(,2*m)

Final Answer

√(,512*m3)=16*m√(,2*m)

Want more problems? Check here!