Simplify square root of 216k^4

Problem

√(,216*k4)

Solution

1. Factor the radicand into its prime factors or perfect square factors.

√(,216*k4)=√(,36⋅6⋅k4)

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

√(,36⋅6⋅k4)=√(,36)⋅√(,k4)⋅√(,6)

3. Evaluate the square roots of the perfect squares.

√(,36)=6

√(,k4)=k2

4. Combine the simplified terms outside the radical and keep the non-square factor inside.

6⋅k2⋅√(,6)=6*k2√(,6)

Final Answer

√(,216*k4)=6*k2√(,6)

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