Evaluate square root of 27/64

Problem

√(,27/64)

Solution

1. Apply the quotient rule for radicals, which states that the square root of a fraction is the square root of the numerator divided by the square root of the denominator.

√(,27/64)=√(,27)/√(,64)

2. Simplify the numerator by factoring the number inside the radical into its prime factors and identifying perfect squares.

√(,27)=√(,9⋅3)

√(,9⋅3)=3√(,3)

3. Simplify the denominator by calculating the square root of the perfect square.

√(,64)=8

4. Combine the results into a single simplified fraction.

(3√(,3))/8

Final Answer

√(,27/64)=(3√(,3))/8

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