Evaluate square root of 192/121

Problem

√(,192/121)

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.

√(,192/121)=√(,192)/√(,121)

2. Simplify the denominator by identifying that 121 is a perfect square.

√(,121)=11

3. Factor the numerator to find the largest perfect square factor of 192

192=64×3

4. Simplify the radical in the numerator by taking the square root of the perfect square factor.

√(,192)=√(,64×3)

√(,192)=8√(,3)

5. Combine the results into a single fraction.

(8√(,3))/11

Final Answer

√(,192/121)=(8√(,3))/11

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