Question

simplify (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

Answer 2

The simplification of the surd given is 83 + 12 √35

What are surds?

Surds are numbers that are placed in square roots and when expressed as a fraction, the values of their decimal form continue till infinity.

From the given information, we are to simplify the given surds to the smallest possible value. i.e.

= (2√5+3√7)^2

= (2√5+3√7) (2√5+3√7)

Using the multiplication rule, we have:

= 4√25 + 6√35 + 6√35 + 9√49

= 4(5) + 12√35 + 9(7)

= 20 + 12 √35 + 63

= 83 + 12 √35

Learn more about calculating surds here:

https://brainly.com/question/840021

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