Evaluate square root of 216

Problem

√(,216)

Solution

1. Identify the number under the radical and look for its prime factors.

√(,216)=√(,2⋅2⋅2⋅3⋅3⋅3)

2. Group the prime factors into pairs of perfect squares to simplify the radical.

√(,216)=√(,(2⋅3)⋅(2⋅3))

3. Simplify the expression by taking the square root of the perfect squares.

√(,216)=√(,36⋅6)

4. Apply the product property of radicals √(,a⋅b)=√(,a)⋅√(,b)

√(,216)=√(,36)⋅√(,6)

5. Calculate the square root of 36.

√(,216)=6√(,6)

Final Answer

√(,216)=6√(,6)

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