Solve sqrt[3]{78*4/60*7*0.42tan(18^circ)}

$$\sqrt[ 3 ]{ \frac{ 78 \cdot 4 }{ 60 \cdot 7 \cdot 0.42 \tan ( 18 ^ { \circ } ) } }$$

Evaluate

$$\frac{200000\sqrt[3]{325}\times 477631953462372261^{\frac{2}{3}}}{477631953462372261}\approx 1.759111326$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt[3]{\frac{78 \cdot 4}{60 \cdot 7 \cdot 0.42 \cdot 0.3249196962329063}}$$

Cancel out 2\times 6 in both numerator and denominator.

$$\sqrt[3]{\frac{2\times 13}{0.3249196962329063\times 0.42\times 5\times 7}}$$

Multiply 2 and 13 to get 26.

$$\sqrt[3]{\frac{26}{0.3249196962329063\times 0.42\times 5\times 7}}$$

Multiply 0.3249196962329063 and 0.42 to get 0.136466272417820646.

$$\sqrt[3]{\frac{26}{0.136466272417820646\times 5\times 7}}$$

Multiply 0.136466272417820646 and 5 to get 0.68233136208910323.

$$\sqrt[3]{\frac{26}{0.68233136208910323\times 7}}$$

Multiply 0.68233136208910323 and 7 to get 4.77631953462372261.

$$\sqrt[3]{\frac{26}{4.77631953462372261}}$$

Expand \frac{26}{4.77631953462372261} by multiplying both numerator and the denominator by 100000000000000000.

$$\sqrt[3]{\frac{2600000000000000000}{477631953462372261}}$$