Question

Помогите с примерами ( желательно с объяснинием)

Answer 1

(3√10 - √5)² = (3√10)² - 2 · 3√10 · √5 + (√5)² = 9·10 - 6√50 + 5 = 95 - 6·5√2 =

= 95 - 30√2.

√(√7 + 4) · √(4 - √7) = √((√7 + 4)·(4 - √7)) = √(4² - (√7)²) = √(16 - 7) = √9 = 3.

Answer 2

${(3 \sqrt{10 } - \sqrt{5})}^{2} = \\ {(3 \sqrt{5 } \sqrt{2} - \sqrt{5})}^{2} = \\ = ( \sqrt{5} ) ^{2} (3 \sqrt{2 } - 1) ^{2} = \\ = 5((3 \sqrt{2} )^{2} - 2(3 \sqrt{2} ) + 1) = \\ = 5(18 - 6 \sqrt{2} + 1) = 5(19 - 6 \sqrt{2} ) = \\ = 95 - 30 \sqrt{2}$

$\sqrt{ \sqrt{7} + 4 } \times \sqrt{4 - \sqrt{7 } } = \sqrt{ {4}^{2} - ( \sqrt{7} ) ^{2} } = \\ \\ = \sqrt{16 - 7} = \sqrt{9} = 3$