Evaluate ( square root of 3- square root of 5)^2

Problem

(√(,3)−√(,5))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=√(,3) and b=√(,5) into the formula.

(√(,3)−√(,5))2=(√(,3))2−2*(√(,3))*(√(,5))+(√(,5))2

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

(√(,3))2=3

(√(,5))2=5

2*(√(,3))*(√(,5))=2√(,15)

5. Combine the constant terms to reach the final result.

3−2√(,15)+5=8−2√(,15)

Final Answer

(√(,3)−√(,5))2=8−2√(,15)

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