Solve sqrt{7*10^-2/2.37}

$$\sqrt { \frac { 7 \times 10 ^ { - 2 } } { 2.37 } }$$

Evaluate

$$\frac{\sqrt{1659}}{237}\approx 0.171860016$$

Solution Steps

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\sqrt{\frac{7\times \frac{1}{100}}{2.37}}$$

Multiply 7 and \frac{1}{100} to get \frac{7}{100}.

$$\sqrt{\frac{\frac{7}{100}}{2.37}}$$

Express \frac{\frac{7}{100}}{2.37} as a single fraction.

$$\sqrt{\frac{7}{100\times 2.37}}$$

Multiply 100 and 2.37 to get 237.

$$\sqrt{\frac{7}{237}}$$

Rewrite the square root of the division \sqrt{\frac{7}{237}} as the division of square roots \frac{\sqrt{7}}{\sqrt{237}}.

$$\frac{\sqrt{7}}{\sqrt{237}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{237}} by multiplying numerator and denominator by \sqrt{237}.

$$\frac{\sqrt{7}\sqrt{237}}{\left(\sqrt{237}\right)^{2}}$$

The square of \sqrt{237} is 237.

$$\frac{\sqrt{7}\sqrt{237}}{237}$$

To multiply \sqrt{7} and \sqrt{237}, multiply the numbers under the square root.

$$\frac{\sqrt{1659}}{237}$$