Evaluate 3 square root of 27

Problem

3√(,27)

Solution

1. Identify the radicand and look for perfect square factors.

2. Factor the number inside the square root into a product of a perfect square and another number.

27=9⋅3

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

√(,27)=√(,9)⋅√(,3)

4. Simplify the square root of the perfect square.

√(,9)=3

5. Substitute the simplified radical back into the original expression.

3√(,27)=3⋅(3√(,3))

6. Multiply the coefficients to find the final value.

3⋅3=9

Final Answer

3√(,27)=9√(,3)

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