Question

ME AJUDE POR FAVOR
Calcule:

a) ³√1728 

b) (2√6)x(√24) 

c) (3/4)³ 

d) (√3)⁴ 

F)(√45)-(√20) 

e - tá na foto
g - tá na foto
h - tá na foto​

Answer 1

Explicação passo-a-passo:

a) Decompondo esse número:

$\sf 1728~~~~~|~~~2$

$\sf ~864~~~~~~|~~~2$

$\sf ~432~~~~~~|~~~2$

$\sf ~216~~~~~~|~~~2$

$\sf ~108~~~~~~|~~~2$

$\sf ~~54~~~~~~~|~~~2$

$\sf ~~27~~~~~~~|~~~3$

$\sf ~~~9~~~~~~~~|~~~3$

$\sf ~~~3~~~~~~~~|~~~3$

$\sf ~~~1$

$\sf 1728=2^6\cdot3^3$

Assim:

$\sf \sqrt[3]{1728}=\sqrt[3]{2^6\cdot3^3}$

$\sf \sqrt[3]{1728}=\sqrt[3]{(2^2)^3\cdot3^3}$

$\sf \sqrt[3]{1728}=2^2\cdot3$

$\sf \sqrt[3]{1728}=4\cdot3$

$\sf \red{\sqrt[3]{1728}=12}$

b)

$\sf 2\sqrt{6}\times\sqrt{24}$

$\sf =2\cdot\sqrt{6\times24}$

$\sf =2\cdot\sqrt{144}$

$\sf =2\cdot12$

$\sf =\red{24}$

c)

$\sf \Big(\dfrac{3}{4}\Big)^3=\dfrac{3^3}{4^3}$

$\sf \Big(\dfrac{3}{4}\Big)^3=\dfrac{3\times3\times3}{4\times4\times4}$

$\sf \red{\Big(\dfrac{3}{4}\Big)^3=\dfrac{27}{64}}$

d)

$\sf (\sqrt{3})^4$

$\sf =\sqrt{3^4}$

$\sf =\sqrt{(3^2)^2}$

$\sf =3^2$

$\sf =3\times3$

$\sf =\red{9}$

e) Lembre-se que $\sf a^{\frac{b}{c}}=\sqrt[c]{a^b}$

$\sf (-64)^{\frac{1}{3}}$

$\sf =\sqrt[3]{(-64)^1}$

$\sf =\sqrt[3]{-64}$

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

$\sf =\sqrt[3]{(-2^2)^3}$

$\sf =-2^2$

$\sf =-2\cdot2$

$\sf =\red{-4}$

f)

$\sf \sqrt{45}-\sqrt{20}$

$\sf =\sqrt{3^2\cdot5}-\sqrt{2^2\cdot5}$

$\sf =3\sqrt{5}-2\sqrt{5}$

$\sf =\red{\sqrt{5}}$

g) Em multiplicação de potências de mesma base, repetimos a base e somamos os expoentes

$\sf (-3)^5\times(-3)^{-1}$

$\sf =(-3)^{5+(-1)}$

$\sf =(-3)^{5-1}$

$\sf =(-3)^{4}$

$\sf =(-3)\times(-3)\times(-3)\times(-3)$

$\sf =(+9)\times(+9)$

$\sf =\red{+81}$

h)

$\sf \Big(\dfrac{\sqrt{24}}{\sqrt{2}}\Big)+3^{\frac{3}{2}}$

$\sf =\dfrac{\sqrt{2}\cdot\sqrt{12}}{\sqrt{2}}+\sqrt[2]{3^3}$

$\sf =\sqrt{12}+\sqrt{3^3}$

$\sf =\sqrt{2^2\cdot3}+\sqrt{3^2\cdot3}$

$\sf =2\sqrt{3}+3\sqrt{3}$

$\sf =\red{5\sqrt{3}}$

Answer 2

A resposta é 5

$5 \sqrt{?}3$