Evaluate ( square root of 5- square root of 7)^2

Problem

(√(,5)−√(,7))2

Solution

1. Identify the expression as a binomial square of the form (a−b)2

2. Apply the formula for the square of a binomial, which is (a−b)2=a2−2*a*b+b2

3. Substitute a=√(,5) and b=√(,7) into the formula.

(√(,5))2−2*(√(,5))*(√(,7))+(√(,7))2

4. Simplify the squared terms and the product of the radicals.

5−2√(,35)+7

5. Combine the constant terms 5 and 7

12−2√(,35)

Final Answer

(√(,5)−√(,7))2=12−2√(,35)

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