Question

Calcule o Valor de Cada Expressão.

Ps: Resposta Com Cálculos.

A)

$\sqrt{6} \times ( \sqrt{15} + \sqrt{60)}$

B)

$\sqrt{3} \times ( \sqrt{54} - \sqrt{6})$

C)

$( \sqrt{3} - 1) \times (\sqrt{3} + 1)$

D)

$(2 - \sqrt{2} ) \times (2 + \sqrt{2})$

E)

$( \sqrt{2} + 1) \times (\sqrt{2} + 1)$

​

Answer 1

Explicação passo-a-passo:

A)

$\sqrt{6} ( \sqrt{15} + \sqrt{60} )$

$\sqrt{6} ( \sqrt{15} + \sqrt{2 {}^{2} \times 15 } )$

$\sqrt{6} ( \sqrt{15} + \sqrt{2 {}^{2} } \sqrt{15} )$

$\sqrt{6} ( \sqrt{15} + 2 \sqrt{15})$

$\sqrt{6} (1 + 2) \sqrt{15}$

$\sqrt{6} \times 3 \sqrt{15}$

$3 \sqrt{15} \sqrt{6}$

$3 \sqrt{90}$

$3 \sqrt{3 {}^{2} \times 10}$

$3 \sqrt{3 {}^{2} } \sqrt{10}$

$3 \times 3 \sqrt{10}$

$9 \sqrt{10}$

B)

$\sqrt{3} ( \sqrt{54} - 6)$

$\sqrt{3} ( \sqrt{3 {}^{2 } \times 6 } - 6)$

$\sqrt{3} ( \sqrt{3 {}^{2} } \sqrt{6} - 6)$

$\sqrt{3} (3 \sqrt{6} - 6)$

$3 \sqrt{6} \sqrt{3} - 6 \sqrt{3}$

$3 \sqrt{18} - 6 \sqrt{3}$

$3 \sqrt{3 {}^{2} \times 2} - 6 \sqrt{3}$

$3 \sqrt{3 {}^{2} } \sqrt{2} - 6 \sqrt{3}$

$3 \times 3 \sqrt{2} - 6 \sqrt{3}$

$9 \sqrt{2} - 6 \sqrt{3}$

C)

$( \sqrt{3} - 1)( \sqrt{3} + 1)$

$( \sqrt{3} ) {}^{2} - (1) {}^{2}$

$3 - 1$

$2$

D)

$(2 - \sqrt{2} )(2 + \sqrt{2} )$

$(2) {}^{2} - ( \sqrt{2} ) {}^{2}$

$4 - 2$

$2$

E)

$( \sqrt{2} + 1)( \sqrt{2} + 1)$

$\sqrt{2} \sqrt{2} + \sqrt{2} + \sqrt{2} + 1$

$\sqrt{4} + \sqrt{2} + \sqrt{2} + 1$

$2 + \sqrt{2} + \sqrt{2} + 1$

$2 + 1 + (1 + 1) \sqrt{2}$

$3 + 2 \sqrt{2}$