Evaluate

Problem

√(,18)/√(,81)

Solution

1. Simplify the denominator by recognizing that 81 is a perfect square.

√(,81)=9

2. Rewrite the expression using the simplified denominator.

√(,18)/9

3. Simplify the numerator by factoring 18 into its largest perfect square factor, which is 9

√(,18)=√(,9⋅2)

4. Apply the product property of radicals to separate the factors.

√(,9⋅2)=√(,9)⋅√(,2)

5. Evaluate the square root of the perfect square factor.

3⋅√(,2)=3√(,2)

6. Substitute the simplified numerator back into the fraction.

(3√(,2))/9

7. Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, 3

(3√(,2)÷3)/(9÷3)=√(,2)/3

Final Answer

√(,18)/√(,81)=√(,2)/3

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