Simplify square root of 54

Problem

√(,54)

Solution

1. Identify the largest perfect square factor of the radicand 54.

2. Factor the number 54 into the product of its largest perfect square factor and another integer.

√(,54)=√(,9⋅6)

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

√(,9⋅6)=√(,9)⋅√(,6)

4. Simplify the square root of the perfect square.

√(,9)⋅√(,6)=3√(,6)

Final Answer

√(,54)=3√(,6)

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