Simplify square root of 64m^3n^3

Problem

√(,64*m3*n3)

Solution

1. Rewrite the expression by breaking the radicand into perfect square factors and remaining factors.

√(,64⋅m2⋅m⋅n2⋅n)

2. Apply the product property of radicals, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,64)⋅√(,m2)⋅√(,n2)⋅√(,m*n)

3. Evaluate the square roots of the perfect squares.

8⋅m⋅n⋅√(,m*n)

4. Combine the terms outside the radical to reach the simplest form.

8*m*n√(,m*n)

Final Answer

√(,64*m3*n3)=8*m*n√(,m*n)

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