Solve sqrt{10/7}*10*4*sin(30)

$$\sqrt{ \frac{ 10 }{ 7 } } \times 10 \times 4 \times \sin ( 30 )$$

Evaluate

$$\frac{20\sqrt{70}}{7}\approx 23.904572187$$

Solution Steps

Multiply 4 and 10 to get 40.

$$40\sqrt{\frac{10}{7}}\sin(30)$$

Rewrite the square root of the division \sqrt{\frac{10}{7}} as the division of square roots \frac{\sqrt{10}}{\sqrt{7}}.

$$40\times \frac{\sqrt{10}}{\sqrt{7}}\sin(30)$$

Rationalize the denominator of \frac{\sqrt{10}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$40\times \frac{\sqrt{10}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\sin(30)$$

The square of \sqrt{7} is 7.

$$40\times \frac{\sqrt{10}\sqrt{7}}{7}\sin(30)$$

To multiply \sqrt{10} and \sqrt{7}, multiply the numbers under the square root.

$$40\times \frac{\sqrt{70}}{7}\sin(30)$$

Get the value of \sin(30) from trigonometric values table.

$$40\times \frac{\sqrt{70}}{7}\times \frac{1}{2}$$

Multiply 40 and \frac{1}{2} to get 20.

$$20\times \frac{\sqrt{70}}{7}$$

Express 20\times \frac{\sqrt{70}}{7} as a single fraction.

$$\frac{20\sqrt{70}}{7}$$