Simplify ( square root of x- square root of 5)^2

Problem

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

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

4. Simplify each term by squaring the roots and combining the product.

(√(,x))2=x

2*(√(,x))*(√(,5))=2√(,5*x)

(√(,5))2=5

5. Combine the simplified terms into the final expression.

x−2√(,5*x)+5

Final Answer

(√(,x)−√(,5))2=x−2√(,5*x)+5

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