Simplify square root of 45x^3

Problem

√(,45*x3)

Solution

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

√(,9⋅5⋅x2⋅x)

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

√(,9)⋅√(,x2)⋅√(,5*x)

3. Simplify the square roots of the perfect squares.

3⋅x⋅√(,5*x)

4. Combine the terms outside the radical.

3*x√(,5*x)

Final Answer

√(,45*x3)=3*x√(,5*x)

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