Simplify square root of 216

Problem

√(,216)

Solution

1. Identify the prime factorization of the number inside the radical.

216=2⋅2⋅2⋅3⋅3⋅3

2. Group the factors into pairs of perfect squares.

216=(2⋅3)⋅(2⋅3)

3. Rewrite the expression by separating the perfect squares from the remaining factors.

√(,216)=√(,36⋅6)

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

√(,216)=√(,36)⋅√(,6)

5. Simplify the square root of the perfect square.

√(,216)=6√(,6)

Final Answer

√(,216)=6√(,6)

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