Solve sqrt{10*tan(37^circ)/0.6}

$$\sqrt{ \frac{ 10 \times \tan ( 37 ^ { \circ } ) }{ 0.6 } }$$

Evaluate

$$\frac{\sqrt{11303310751541913}}{30000000}\approx 3.543900982$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt{\frac{10 \cdot 0.7535540501027942}{0.6}}$$

Multiply 10 and 0.7535540501027942 to get 7.535540501027942.

$$\sqrt{\frac{7.535540501027942}{0.6}}$$

Expand \frac{7.535540501027942}{0.6} by multiplying both numerator and the denominator by 1000000000000000.

$$\sqrt{\frac{7535540501027942}{600000000000000}}$$

Reduce the fraction \frac{7535540501027942}{600000000000000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{3767770250513971}{300000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{3767770250513971}{300000000000000}} as the division of square roots \frac{\sqrt{3767770250513971}}{\sqrt{300000000000000}}.

$$\frac{\sqrt{3767770250513971}}{\sqrt{300000000000000}}$$

Factor 300000000000000=10000000^{2}\times 3. Rewrite the square root of the product \sqrt{10000000^{2}\times 3} as the product of square roots \sqrt{10000000^{2}}\sqrt{3}. Take the square root of 10000000^{2}.

$$\frac{\sqrt{3767770250513971}}{10000000\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{3767770250513971}}{10000000\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3767770250513971}\sqrt{3}}{10000000\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3767770250513971}\sqrt{3}}{10000000\times 3}$$

To multiply \sqrt{3767770250513971} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{11303310751541913}}{10000000\times 3}$$

Multiply 10000000 and 3 to get 30000000.

$$\frac{\sqrt{11303310751541913}}{30000000}$$