Question

Simplify (2√5+3√7)^2

Answer 1

(2 sq. root 5 + 3 sq. root 7)(2 sq. root 5 + 3 sq. root 7)

4•sq root 25 + 6 sq. root 35 + 6 sq. root 35 + 9 sq. root 49

4 • 5 + 12 sq. root 35 + 9 • 7

20 + 12 sq. root 35 + 63.

I believe this would be the solution.

Answer 2

The answer is: 83 + 12√35

(a + b)² = a² + 2ab + b²

In (2√5 + 3√7)², a = 2√5, b = 3√7

Just substitute a and b:
(a + b)² = a² + 2ab + b² = (2√5)² + 2 * 2√5 * 3√7 + (3√7)² = 
            = 2²√5² + 2 * 2 * 3 * √5 * √7 + 3²√7² =
            = 4 * 5 + 12 * √(5*7) + 9 * 7 =
            = 20 + 12 *√35 + 63 =
            = 83 + 12√35