Question

Determine o valor da expressão:

A) ✓3 • (✓18 + ✓32) - ✓114 ÷ ✓19 =

B) ✓12 • (✓3 - ✓12) + ✓2 • (✓6 - ✓18)

Answer 1

a)
$\sqrt{3} \times ( \sqrt{18} + \sqrt{32} ) + \sqrt{2} \times ( \sqrt{6} - \sqrt{18}$
Vamo Fatorando


$\sqrt{3 } \times ( \sqrt{ {3}^{2} \times 2} + \sqrt{ {4}^{2} \times 2}) + \sqrt{2} \times ( \sqrt{6} - \sqrt{ {3}^{2} \times 2 }$

Cancele o indice com o expoentes

$\sqrt{3} \times ( 3 \sqrt{2} + 4 \sqrt{2} ) + \sqrt{2} \times ( \sqrt{6} - 3 \sqrt{2} )$

Some alguns termos similares e faça a distribuitiva

$\sqrt{3} \times 7 \sqrt{2} + \sqrt{12} - 6$
Simplifique A Raiz de 12 e Multiplique

$7\sqrt{6} + \sqrt{ {2}^{2} + 3 } - 6 \\ 7 \sqrt{6} + 2 \sqrt{3} - 6$
b)

$\sqrt{12} \times ( \sqrt{3} - \sqrt{12} ) + \sqrt{2} \times ( \sqrt{6} - \sqrt{18} )$
Fatore


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

Cancele indice com o expoente

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

Some E aplique a propriedade distribuitiva

$\sqrt{12} \times ( - \sqrt{3} ) + \sqrt{12} - 6$
Multiplique e fatore

$- \sqrt{36} + \sqrt{ {2}^{2} \times 3 } - 6$
Cancele Indice com expoente

$- \sqrt{36} + 2 \sqrt{3} - 6$
Extraia a raiz de 36

$- 6 +2 \sqrt{3} - 6$
Some -6 com -6

$- 12 + 2\sqrt{ 3}$