Solve sqrt{3/3.5}

$$\sqrt { \frac { 3 } { 3.5 } }$$

Evaluate

$$\frac{\sqrt{42}}{7}\approx 0.9258201$$

Solution Steps

Expand \frac{3}{3.5} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{30}{35}}$$

Reduce the fraction \frac{30}{35} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{6}{7}}$$

Rewrite the square root of the division \sqrt{\frac{6}{7}} as the division of square roots \frac{\sqrt{6}}{\sqrt{7}}.

$$\frac{\sqrt{6}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{6}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{6}\sqrt{7}}{7}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{7}$$