Solve sqrt{3.70/9.8}

$$\sqrt{ \frac{ 3.70 }{ 9.8 } }$$

Evaluate

$$\frac{\sqrt{74}}{14}\approx 0.614451805$$

Solution Steps

Expand \frac{3.7}{9.8} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{37}{98}}$$

Rewrite the square root of the division \sqrt{\frac{37}{98}} as the division of square roots \frac{\sqrt{37}}{\sqrt{98}}.

$$\frac{\sqrt{37}}{\sqrt{98}}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{\sqrt{37}}{7\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{37}}{7\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{37}\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{37}\sqrt{2}}{7\times 2}$$

To multiply \sqrt{37} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{74}}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{\sqrt{74}}{14}$$