Question

Calcule ( não consegui digitar pois são números elevados etc.)

Answer 1

Explicação passo-a-passo:

.

$a) \dfrac{ \sqrt{3} }{3} \times 5 \sqrt{12} \times \dfrac{ \sqrt{8} }{10} \times 3 \sqrt{2}$

$\sqrt{3} \times 2 \sqrt{3} \times \dfrac{2 \sqrt{2} }{2} \times \sqrt{2}$

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

$3 \times 2 \times 2$

$12$

.

$b)2 \sqrt{8} \times 3 \sqrt{2} \times \sqrt[3]{27}$

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

$2 \times 2 \times 2 \times 3 \times 3$

$72$

.

$c) \sqrt[3]{2} \times \sqrt[3]{16} \times 3 \sqrt[3]{2}$

$\sqrt[3]{4} \times 2 \sqrt[3]{2} \times 3$

$6 \sqrt[3]{8}$

$6 \times 2$

$12$

.

$d)3 \sqrt[4]{2} \times 2 \sqrt[4]{3} \times \sqrt[4]{8}$

$6 \sqrt[4]{48}$

$12 \sqrt[4]{3}$

.

$e)5 \sqrt{27} \times \sqrt[3]{9}$

$5 \sqrt[6]{27 {}^{3} } \sqrt[6]{9 {}^{2} }$

$5 \sqrt[6]{27 {}^{3} \times 9 {}^{2} }$

$5 \sqrt[6]{3 {}^{9} \times 3 {}^{4} }$

$5 \sqrt[6]{3 {}^{13} }$

$5 \times 3 {}^{2} \sqrt[6]{3}$

$5 \times 9 \sqrt[6]{3}$

$45 \sqrt[6]{3}$

.

$f)2 \sqrt{2} \times 4 \sqrt[4]{8} \times 8 \sqrt[8]{4}$

$2 \sqrt[8]{2 {}^{4} } \times 4 \sqrt[8]{8 {}^{2} } \times 8 \sqrt[8]{4}$

$2 \sqrt[8]{2 {}^{4} \times 8 {}^{2} \times 4 \times 4 \times 8 }$

$2 \sqrt[8]{2 {}^{4} \times 2 {}^{6} \times 2 {}^{2} \times 4 \times 8 }$

$2 \sqrt[8]{2 {}^{12} \times 4 \times 8 }$

$2 \sqrt{2 {}^{3} \times 4 \times 8}$

$2 \times 2 \sqrt{2} \times 4 \times 8$

$128 \sqrt{2}$

Answer 2

Oie, tudo bom?

a)

$= \frac{ \sqrt{3} }{3} \: . \: 5 \sqrt{12} \: . \: \frac{ \sqrt{8} }{10} \: . \: 3 \sqrt{2}$

$= \sqrt{3} \: . \: 2 \sqrt{3} \: . \: \frac{2 \sqrt{2} }{2} \: . \: \sqrt{2}$

$= 3 \: . \: 2 \sqrt{2} \sqrt{2}$

$= 3 \: . \: 2 \: . \: 2$

$\boxed { = 12}$

b)

$= 2 \sqrt{8} \: . \: 3 \sqrt{2} \: . \: \sqrt[3]{27}$

$= 2 \: . \: 2 \sqrt{2} \: . \: 3 \sqrt{2} \: . \: 3$

$= 2 \: . \: 2 \: . \: 2 \: . \: 3 \: . \: 3$

$\boxed { =72 }$

c)

$= \sqrt[3]{2} \: . \: \sqrt[3]{16} \: . \: 3 \sqrt[3]{2}$

$= \sqrt[3]{4} \: . \: 2 \sqrt[3]{2} \: . \: 3$

$= \sqrt[3]{4 \: . \: 3} \: . \: 6$

$= \sqrt[3]{8} \: . \: 6$

$= 6 \sqrt[3]{8}$

$= 6 \: . \: 2$

$\boxed { =12 }$

d)

$= 3 \sqrt[4]{2} \: . \: 2 \sqrt[4]{3} \: . \: \sqrt[4]{8}$

$= 6 \sqrt[4]{2 \: . \: 3 \: . \: 8}$

$= 6 \sqrt[4]{48}$

$= 6 \sqrt[4]{2 {}^{4} \: . \: 3}$

$= 6 \sqrt[4]{2 {}^{4} } \sqrt[4]{3}$

$= 6 \: . \: 2 \sqrt[4]{3}$

$=12 \sqrt[4]{3}$

$\boxed {≈15,79 }$

e)

$= 5 \sqrt{27} \: . \: \sqrt[3]{9}$

$= 5 \sqrt[6]{27 {}^{3} } \sqrt[6]{9 {}^{2} }$

$= 5 \sqrt[6]{27 {}^{3} \: . \: 9 {}^{2} }$

$= 5 \sqrt[6]{3 {}^{9} \: . \: 3 {}^{4} }$

$= 5 \sqrt[6]{3 {}^{13} }$

$= 5 \: . \: 3 {}^{2} \sqrt[6]{3}$

$= 5 \: . \: 9 \sqrt[6]{3}$

$= 45 \sqrt[6]{3}$

$\boxed {≈54,04 }$

f)

$= 2 \sqrt{2} \: . \: 4 \sqrt[4]{8} \: . \: 8 \sqrt[8]{4}$

$= 2 \sqrt[8]{2 {}^{4} } \: . \: 4 \sqrt[8]{8 {}^{2} } \: . \: 8 \sqrt[8]{4}$

$= 2 \sqrt[8]{2 {}^{4} \: . \: 8 {}^{2} \: . \: 4 } \: . \: 4 \: . \: 8$

$= 2 \sqrt[8]{2 {}^{4} \: . \: 2 {}^{6} \: . \: 2 {}^{2} } \: . \: 4 \: . \: 8$

$= 2 \sqrt[8]{2 {}^{12} } \: . \: 4 \: . \: 8$

$= 2 \sqrt{2 {}^{3} } \: . \: 4 \: . \: 8$

$= 2 \: . \: 2 \sqrt{2} \: . \: 4 \: . \: 8$

$= 128 \sqrt{2}$

$\boxed {≈181,01 }$

Att. NBA YoungBoy