Simplify square root of 216v

Problem

√(,216*v)

Solution

1. Factor the number inside the radical to find the largest perfect square divisor.

216=36⋅6

2. Rewrite the expression by substituting the factored form into the square root.

√(,36⋅6⋅v)

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

√(,36)⋅√(,6*v)

4. Simplify the square root of the perfect square.

6√(,6*v)

Final Answer

√(,216*v)=6√(,6*v)

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