Solve sqrt{2-3.2/3.2-5}

$$\sqrt { \frac { 2 - 3.2 } { 3.2 - 5 } }$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Subtract 3.2 from 2 to get -1.2.

$$\sqrt{\frac{-1.2}{3.2-5}}$$

Subtract 5 from 3.2 to get -1.8.

$$\sqrt{\frac{-1.2}{-1.8}}$$

Expand \frac{-1.2}{-1.8} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{-12}{-18}}$$

Reduce the fraction \frac{-12}{-18} to lowest terms by extracting and canceling out -6.

$$\sqrt{\frac{2}{3}}$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3}$$