Question

What is the following quotient? 6-3(3 √8)/3 √9

Answer 1

Answer:

The correct option is A) $2\sqrt[3]{3}-{\sqrt[3]{18}$

Step-by-step explanation:

Consider the provided expression.

$\frac{\left(6-3\left(\sqrt[3]{6}\right)\right)}{\sqrt[3]{9}}$

Rationalize by multiplying conjugate $\frac{9^{\frac{2}{3}}}{9^{\frac{2}{3}}}$

$\frac{\left(6-3\sqrt[3]{6}\right)\cdot \:9^{\frac{2}{3}}}{\sqrt[3]{9}\cdot \:9^{\frac{2}{3}}}$

$\frac{9^{\frac{2}{3}}\cdot \:3\left(2-\sqrt[3]{6}\right)}{9}$

$\frac{9^{\frac{2}{3}}\left(2-\sqrt[3]{6}\right)}{3}$

$\frac{3^{\frac{4}{3}}\left(2-\sqrt[3]{6}\right)}{3}$

$3^{\frac{1}{3}}\left(2-\sqrt[3]{6}\right)$

$2\sqrt[3]{3}-3^{\frac{2}{3}}\sqrt[3]{2}$

$2\sqrt[3]{3}-{\sqrt[3]{18}$

Hence, the correct option is A) $2\sqrt[3]{3}-{\sqrt[3]{18}$

Answer 2

Answer:

Factor the numerator and denominator and cancel the common factors.

Exact Form:

2

3

√

3

−

3

√

18

Decimal Form:

0.26375774