Question

Simplify the following expression.

1) (5+√7)(2+√5)
2) (5+√5)(5-√5)​

Answer 1

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1.

$(5 + \sqrt{7}) (2 + \sqrt{5} ) \\ \\ = 5 \times 2 + 5 \times \sqrt{5} + \sqrt{7} \times 2 + \sqrt{7} \times 5 \\ \\ = 10 + 5 \sqrt{5} + 2 \sqrt{7} + \sqrt{35} \: ans$

2.

$(5 + \sqrt{5} )(5 - \sqrt{5} ) \\ \\ =formula \: used \: = \\ (a + b)(a - b) = a {}^{2} - b {}^{2} \\ 5 {}^{2} - ( \sqrt{5} ) {}^{2} \\ 25 - 5 \\ 20$

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