Question

qual o valor da razão da questão na imagem
preciso urgente

Answer 1

Explicação passo-a-passo:

• Valor de A

Decompondo 1728:

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

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

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

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

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

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

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

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

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

$\sf 1$

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

Temos:

$\sf A=\sqrt[3]{1728}$

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

$\sf A=\sqrt[3]{(2^2)^3\cdot(3^1)^3}$

$\sf A=2^2\cdot3^1$

$\sf A=4\cdot3$

$\sf \red{\sf A=12}$

• Valor de B

Decompondo 64:

$\sf 64~~~~~|~~2$

$\sf 32~~~~~|~~2$

$\sf 16~~~~~|~~2$

$\sf 8~~~~~~~|~~2$

$\sf 4~~~~~~~|~~2$

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

$\sf 1$

Então, $\sf 64=2^6$

Desse modo:

$\sf B=\sqrt[6]{64}$

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

$\sf \red{B=2}$

Logo:

$\sf \dfrac{A}{B}=\dfrac{12}{2}$

$\boxed{\red{\sf \dfrac{A}{B}=6}}$