Simplify ( square root of x+2 square root of 3)^2

Problem

(√(,x)+2√(,3))2

Solution

1. Identify the expression as a binomial square of the form (a+b)2 where a=√(,x) and b=2√(,3)

2. Apply the formula for the square of a binomial: (a+b)2=a2+2*a*b+b2

3. Substitute the values into the formula:

(√(,x))2+2*(√(,x))*(2√(,3))+(2√(,3))2

4. Simplify each term individually:

(√(,x))2=x

2*(√(,x))*(2√(,3))=4√(,3*x)

(2√(,3))2=4⋅3=12

5. Combine the simplified terms to reach the final expression.

Final Answer

(√(,x)+2√(,3))2=x+4√(,3*x)+12

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