Question

Simplify
$(8 + \sqrt{5)}(8 - \sqrt{5)}$
$(10+\sqrt{3})(6 + \sqrt{2)}$
$(3+{ \sqrt{11} }^{2} ) + (3 - { \sqrt{11} }^{2} )$
​please give correct answer

Answer 1

$since \\ {a }^{2} - {b}^{2} = (a - b)(a + b)$

$a) \: \: (8 + \sqrt{5)}(8 - \sqrt{5)} \\ = {8}^{2} - { \sqrt{5} }^{2} \\ = 64 - 5 = 59$

$b) \: \: (10+\sqrt{3})(6 + \sqrt{2)} \\ = 10(6 + \sqrt{2} ) + \sqrt{3} (6 + \sqrt{2} ) \\ = 60 + 10 \sqrt{2} + 6 \sqrt{3} + \sqrt{6}$

$c) \: \: (3+{ \sqrt{11} }^{2} ) + (3 - { \sqrt{11} }^{2} ) \\ = {3}^{2} - { \sqrt{11} }^{2} \\ = 9 - 11 = - 2$

hope it will help u ✨☺️