Solve sqrt{37/9.8}*24div20

$$\sqrt{ \frac{ 37 }{ 9.8 } } \times 24 \div 20$$

Evaluate

$$\frac{6\sqrt{185}}{35}\approx 2.331680659$$

Solution Steps

Expand \frac{37}{9.8} by multiplying both numerator and the denominator by 10.

$$\frac{24\sqrt{\frac{370}{98}}}{20}$$

Reduce the fraction \frac{370}{98} to lowest terms by extracting and canceling out 2.

$$\frac{24\sqrt{\frac{185}{49}}}{20}$$

Rewrite the square root of the division \sqrt{\frac{185}{49}} as the division of square roots \frac{\sqrt{185}}{\sqrt{49}}.

$$\frac{24\times \frac{\sqrt{185}}{\sqrt{49}}}{20}$$

Calculate the square root of 49 and get 7.

$$\frac{24\times \frac{\sqrt{185}}{7}}{20}$$

Express 24\times \frac{\sqrt{185}}{7} as a single fraction.

$$\frac{\frac{24\sqrt{185}}{7}}{20}$$

Express \frac{\frac{24\sqrt{185}}{7}}{20} as a single fraction.

$$\frac{24\sqrt{185}}{7\times 20}$$

Cancel out 4 in both numerator and denominator.

$$\frac{6\sqrt{185}}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$\frac{6\sqrt{185}}{35}$$