Simplify square root of 27

Problem

√(,27)

Solution

1. Identify the radicand and look for the largest perfect square factor of 27

2. Factor the number 27 into the product of a perfect square and another integer.

√(,27)=√(,9⋅3)

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

√(,9⋅3)=√(,9)⋅√(,3)

4. Simplify the square root of the perfect square 9

√(,9)⋅√(,3)=3√(,3)

Final Answer

√(,27)=3√(,3)

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