Simplify square root of 200m^4n

Problem

√(,200*m4*n)

Solution

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

√(,100⋅2⋅m4⋅n)

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

√(,100)⋅√(,m4)⋅√(,2*n)

3. Evaluate the square roots of the perfect squares.

10⋅m2⋅√(,2*n)

4. Combine the terms outside the radical.

10*m2√(,2*n)

Final Answer

√(,200*m4*n)=10*m2√(,2*n)

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