Solve frac{sqrt{3,2}-sqrt{1,8}}{sqrt{10}}

$$\frac { \sqrt { 3,2 } - \sqrt { 1,8 } } { \sqrt { 10 } }$$

Evaluate

$$\frac{\sqrt{2}}{10}\approx 0.141421356$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{3,2}-\sqrt{1,8}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\left(\sqrt{3,2}-\sqrt{1,8}\right)\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\left(\sqrt{3,2}-\sqrt{1,8}\right)\sqrt{10}}{10}$$

Use the distributive property to multiply \sqrt{3,2}-\sqrt{1,8} by \sqrt{10}.

$$\frac{\sqrt{3,2}\sqrt{10}-\sqrt{1,8}\sqrt{10}}{10}$$

To multiply \sqrt{3,2} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{32}-\sqrt{1,8}\sqrt{10}}{10}$$

To multiply \sqrt{1,8} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{32}-\sqrt{18}}{10}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{4\sqrt{2}-\sqrt{18}}{10}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{4\sqrt{2}-3\sqrt{2}}{10}$$

Combine 4\sqrt{2} and -3\sqrt{2} to get \sqrt{2}.

$$\frac{\sqrt{2}}{10}$$