Question

Simplify. Show your work.
(2√(5)+3√(7))^2

Answer 1

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

Explanation: