Simplify

Problem

√(,5*a3*b)⋅√(,10*a*b)

Solution

1. Apply the product property of radicals to combine the two square roots into a single radical expression.

√(,5*a3*b⋅10*a*b)

2. Multiply the terms inside the radical by grouping coefficients and variables.

√(,50*a4*b2)

3. Factor out the perfect squares from the radicand to prepare for simplification.

√(,25⋅2⋅a4⋅b2)

4. Simplify the radical by taking the square root of each perfect square factor (25 a4 and b2.

5*a2*b√(,2)

Final Answer

√(,5*a3*b)⋅√(,10*a*b)=5*a2*b√(,2)

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