Solve sqrt[3]{2+10/27}=4/3/3,sqrt[3]{33/8}=frac{3}{2}

$$\sqrt[ 3 ] { 2 + \frac { 10 } { 27 } } = \frac { \frac { 4 } { 3 } } { 3 } , \sqrt[ 3 ] { 3 \frac { 3 } { 8 } } = \frac { 3 } { 2 }$$

Verify

Solution Steps

Add 2 and \frac{10}{27} to get \frac{64}{27}.

$$\sqrt[3]{\frac{64}{27}}=\frac{\frac{4}{3}}{3}\text{ and }\sqrt[3]{\frac{3\times 8+3}{8}}=\frac{3}{2}$$

Calculate \sqrt[3]{\frac{64}{27}} and get \frac{4}{3}.

$$\frac{4}{3}=\frac{\frac{4}{3}}{3}\text{ and }\sqrt[3]{\frac{3\times 8+3}{8}}=\frac{3}{2}$$

Express \frac{\frac{4}{3}}{3} as a single fraction.

$$\frac{4}{3}=\frac{4}{3\times 3}\text{ and }\sqrt[3]{\frac{3\times 8+3}{8}}=\frac{3}{2}$$

Multiply 3 and 3 to get 9.

$$\frac{4}{3}=\frac{4}{9}\text{ and }\sqrt[3]{\frac{3\times 8+3}{8}}=\frac{3}{2}$$

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{12}{9}=\frac{4}{9}\text{ and }\sqrt[3]{\frac{3\times 8+3}{8}}=\frac{3}{2}$$

Compare \frac{12}{9} and \frac{4}{9}.

$$\text{false}\text{ and }\sqrt[3]{\frac{3\times 8+3}{8}}=\frac{3}{2}$$

Multiply 3 and 8 to get 24.

$$\text{false}\text{ and }\sqrt[3]{\frac{24+3}{8}}=\frac{3}{2}$$

Add 24 and 3 to get 27.

$$\text{false}\text{ and }\sqrt[3]{\frac{27}{8}}=\frac{3}{2}$$

Calculate \sqrt[3]{\frac{27}{8}} and get \frac{3}{2}.

$$\text{false}\text{ and }\frac{3}{2}=\frac{3}{2}$$

Compare \frac{3}{2} and \frac{3}{2}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$