Question

Calcule:


OBS: não consegui digitar tudo no LaTeX...

Answer 1

Explicação passo-a-passo:

.

$a)2 \sqrt{8} - 3 \sqrt{18} + \sqrt{32} - 2 \sqrt{50}$

$4 \sqrt{2} - 9 \sqrt{2} + 2 {}^{2} \sqrt{2} - 10 \sqrt{2}$

$4 \sqrt{2} - 9 \sqrt{2} + 4 \sqrt{2} - 10 \sqrt{2}$

$(4 - 9 + 4 - 10) \sqrt{2}$

$- 11 \sqrt{2}$

.

$b) \sqrt{32} - 2 \sqrt{12} - \sqrt{75} + 3 \sqrt{72}$

$2 {}^{2} \sqrt{2} - 4 \sqrt{3} - 5 \sqrt{3} + 18 \sqrt{2}$

$4 \sqrt{2} - 4 \sqrt{3} - 5 \sqrt{3} + 18 \sqrt{2}$

$(4 + 18) \sqrt{2} + ( - 4 - 5) \sqrt{3}$

$22 \sqrt{2} - 9 \sqrt{3}$

.

$c)5 \sqrt{24} - 3 \sqrt{16} + \sqrt{54} - \sqrt{36}$

$10 \sqrt{6} - 3 \sqrt{6} + 3 \sqrt{6} - 6$

Elimine os opostos

$10 \sqrt{6} - 6$

.

$d)5 \sqrt{6} + \sqrt{25} - 2 \sqrt{24} - \sqrt{96} - 3 \sqrt{16}$

$5 \sqrt{6} + 5 - 4 \sqrt{6} - 4 \sqrt{6} - 3 \times 4$

$5 \sqrt{6} + 5 - 4 \sqrt{6} - 4 \sqrt{6} - 12$

$(5 - 4 - 4) \sqrt{6} + (5 - 12)$

$- 3 \sqrt{6} - 7$

.

$e)5 \sqrt{2} - 2 \sqrt{5} + \sqrt{50} - 2 \sqrt{20} + \sqrt{500}$

$5 \sqrt{2} - 2 \sqrt{5} + 5 \sqrt{2} - 4 \sqrt{5} + 10 \sqrt{5}$

$(5 + 5) \sqrt{2} + ( - 2 - 4 + 10) \sqrt{5}$

$10 \sqrt{2} + 4 \sqrt{5}$

.

$f) - \dfrac{1}{2} \sqrt{44} + 3 \sqrt{99} - \dfrac{2}{3} \sqrt{11} - \dfrac{1}{4} \sqrt{1100}$

$- \dfrac{ \sqrt{11} }{1} + \dfrac{9 \sqrt{11} }{1} - \dfrac{2 \times 2 \sqrt{11} }{2 \times 3} - \dfrac{3 \times 5 \sqrt{11} }{3 \times 2}$

$- \dfrac{6 \sqrt{11} }{6 \times 1} + \dfrac{6 \times 9 \sqrt{11} }{6 \times 1} - \dfrac{4 \sqrt{11} }{6} - \dfrac{15 \sqrt{11} }{6}$

$- \dfrac{6 \sqrt{11} + 54 \sqrt{11} - 4 \sqrt{11} - 15 \sqrt{11} }{6}$

$\dfrac{( - 6 + 54 - 4 - 15) \sqrt{11} }{6}$

$\dfrac{29 \sqrt{11} }{6}$

Answer 2

Oie, tudo bom?

a)

$= 2 \sqrt{8} - 3 \sqrt{18} + \sqrt{32} - 2 \sqrt{50}$

$= 4 \sqrt{2} - 9 \sqrt{2} + 2 {}^{2} \sqrt{2} - 10 \sqrt{2}$

$= 4 \sqrt{2} - 9 \sqrt{2} + 4 \sqrt{2} - 10 \sqrt{2}$

$= (4 - 9 + 4 - 10) \sqrt{2}$

$\boxed{ = - 11 \sqrt{2} }$

b)

$= \sqrt{32} - 2 \sqrt{12} - \sqrt{75} + 3 \sqrt{72}$

$= 2 {}^{2} \sqrt{2} - 4 \sqrt{3} - 5 \sqrt{3} + 18 \sqrt{2}$

$= 4 \sqrt{2} - 4 \sqrt{3} - 5 \sqrt{3} + 18 \sqrt{2}$

$=(4 + 18) \sqrt{2} - ( - 4 - 5) \sqrt{3}$

$\boxed{ = 22 \sqrt{2} - 9 \sqrt{3} }$

c)

$= 5 \sqrt{24} - 3 \sqrt{6} + \sqrt{54} - \sqrt{36}$

$= 10 \sqrt{6} - 3 \sqrt{6} + 3 \sqrt{6} - 6$

$\boxed{ = 10 \sqrt{6} - 6}$

d)

$= 5 \sqrt{6} + \sqrt{25} - 2 \sqrt{24} - \sqrt{96} - 3 \sqrt{16}$

$= 5 \sqrt{6} + 5 - 4 \sqrt{6} - 4 \sqrt{6} - 3 \: . \: 4$

$= 5 \sqrt{6} + 5 - 4 \sqrt{6} - 4 \sqrt{6} - 12$

$= (5 - 4 - 4) \sqrt{6} + 5 - 12$

$\boxed{ = - 3 \sqrt{6} - 7}$

e)

$= 5 \sqrt{2} - 2 \sqrt{5} + \sqrt{50} - 2 \sqrt{20} + \sqrt{500}$

$= 5 \sqrt{2} - 2 \sqrt{5} + 5 \sqrt{2} - 4 \sqrt{5} + 10 \sqrt{5}$

$= (5 + 5) \sqrt{2} + ( - 2 - 4 + 10) \sqrt{5}$

$\boxed{ = 10 \sqrt{2} + 4\sqrt{5} }$

f)

$= - \frac{1}{2} \sqrt{44} + 3 \sqrt{99} - \frac{2}{3} \sqrt{11} - \frac{1}{2} \sqrt{1100}$

$= - \sqrt{11} + 9 \sqrt{11} - \frac{2 \sqrt{11} }{3} - \frac{5 \sqrt{11} }{2}$

$= - \frac{ \sqrt{11} }{1} + \frac{9 \sqrt{11} }{1} - \frac{2 \: . \: 2 \sqrt{11} }{2 \: . \: 3} - \frac{3 \: . \: 5 \sqrt{11} }{3 \: . \: 2}$

$= - \frac{6 \sqrt{11} }{6 \: . \: 1} + \frac{6 \: . \: 9 \sqrt{11} }{6 \: . \: 1} - \frac{4 \sqrt{11} }{6} - \frac{15 \sqrt{11} }{6}$

$= - \frac{6 \sqrt{11} }{6} + \frac{54 \sqrt{11} }{6} - \frac{4 \sqrt{11} }{6} - \frac{15 \sqrt{11} }{6}$

$= \frac{ - 6 \sqrt{11} + 54 \sqrt{11} - 4 \sqrt{11} - 15 \sqrt{11} }{6}$

$= \frac{( - 6 + 54 - 4 - 15) \sqrt{11} }{6}$

$\boxed{ = \frac{29 \sqrt{11} }{6} }$

Att. NBA YoungBoy