Evaluate

Problem

(√(,5)−√(,7))/(√(,35)−√(,34))

Solution

1. Identify the expression as a fraction involving square roots in both the numerator and the denominator.

2. Rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is √(,35)+√(,34)

3. Apply the difference of squares formula (a−b)*(a+b)=a2−b2 to the denominator.

(√(,35)−√(,34))*(√(,35)+√(,34))=35−34

4. Simplify the denominator to 1

35−34=1

5. Distribute the terms in the numerator.

(√(,5)−√(,7))*(√(,35)+√(,34))=√(,5)√(,35)+√(,5)√(,34)−√(,7)√(,35)−√(,7)√(,34)

6. Simplify the radicals by factoring out perfect squares where possible.

√(,5)√(,35)=√(,5⋅5⋅7)=5√(,7)

√(,7)√(,35)=√(,7⋅7⋅5)=7√(,5)

7. Combine the simplified terms into the final expression.

5√(,7)+√(,170)−7√(,5)−√(,238)

Final Answer

(√(,5)−√(,7))/(√(,35)−√(,34))=5√(,7)−7√(,5)+√(,170)−√(,238)

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