Question

find the cube roots of the following: ( a)216/729 ( b) -343/512 (c)10648/12167 ( d) 4913/-10648 ( e) -2744/3375 ( h) 686/-3456​

Answer 1

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Answer 2

Answer:

The cube roots of the given numbers are

a) $\frac{2}{3}$

b) $\frac{-7}{8}$

c) $\frac{22}{23}$

d) $\frac{-17}{22}$

e) $\frac{-14}{15}$

h) $\frac{-7}{12}$

Step-by-step explanation:

Given some rational numbers.

We need to find the cube roots of them.

Cube root is the number that needs to be multiplied three times to get the original number.

a) $\frac{216}{729}$

Cube root of the following number is

$\sqrt[3]{\frac{216}{729}}=\sqrt[3]{\frac{6^3}{9^3}}$

$=\frac{6}{9}$

$=\frac{2}{3}$

The cube root of $\frac{216}{729}$ is $\frac{2}{3}$.

b) $\frac{-343}{512}$

Cube root of the following number is

$\sqrt[3]{\frac{-343}{512}}=\sqrt[3]{\frac{(-7)^3}{8^3}}$

$=\frac{-7}{8}$

The cube root of $\frac{-343}{512}$ is $\frac{-7}{8}$.

c) $\frac{10648}{12167}$

Cube root of the following number is

$\sqrt[3]{\frac{10648}{12167}}=\sqrt[3]{\frac{22^3}{23^3}}$

$=\frac{22}{23}$

The cube root of $\frac{10648}{12167}$ is $\frac{22}{23}$.

d) $\frac{4913}{-10648}$

Cube root of the following number is

$\sqrt[3]{\frac{4913}{-10648}}=\sqrt[3]{\frac{17^3}{-22^3}}$

$=\frac{17}{-22}$

The cube root of $\frac{4913}{-10648}$ is $\frac{-17}{22}$.

e) $\frac{-2744}{3375}$

Cube root of the following number is

$\sqrt[3]{\frac{-2744}{3375}}=\sqrt[3]{\frac{(-14)^3}{15^3}}$

$=\frac{-14}{15}$

The cube root of $\frac{-2744}{3375}$ is $\frac{-14}{15}$.

h) $\frac{686}{-3456}$

Cube root of the following number is

$\sqrt[3]{\frac{686}{-3456}}=\sqrt[3]{\frac{343}{-1728}}=\sqrt[3]{\frac{7^3}{(-12)^3}}$

$=\frac{7}{-12}$

The cube root of $\frac{686}{-3456}$ is $\frac{-7}{12}$.