Evaluate 3 square root of 8

Problem

3√(,8)

Solution

1. Identify the expression as a product of a constant and a square root.

2. Factor the radicand 8 into its prime factors to find perfect squares.

8=4⋅2

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

3√(,8)=3√(,4⋅2)

3√(,8)=3√(,4)⋅√(,2)

4. Simplify the square root of the perfect square 4

√(,4)=2

5. Multiply the coefficients to find the final simplified form.

3⋅2⋅√(,2)=6√(,2)

Final Answer

3√(,8)=6√(,2)

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