Solve sqrt[3]{21/9-6*14/3+10/3-4}

$$\sqrt[ 3 ] { \frac { 21 } { 9 } - 6 \times \frac { 14 } { 3 } + \frac { 10 } { 3 } - 4 }$$

Evaluate

$$-\frac{\sqrt[3]{79}\times 3^{\frac{2}{3}}}{3}\approx -2.975102587$$

Solution Steps

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

$$\sqrt[3]{\frac{7}{3}-6\times \frac{14}{3}+\frac{10}{3}-4}$$

Multiply 6 and \frac{14}{3} to get 28.

$$\sqrt[3]{\frac{7}{3}-28+\frac{10}{3}-4}$$

Subtract 28 from \frac{7}{3} to get -\frac{77}{3}.

$$\sqrt[3]{-\frac{77}{3}+\frac{10}{3}-4}$$

Add -\frac{77}{3} and \frac{10}{3} to get -\frac{67}{3}.

$$\sqrt[3]{-\frac{67}{3}-4}$$

Subtract 4 from -\frac{67}{3} to get -\frac{79}{3}.

$$\sqrt[3]{-\frac{79}{3}}$$