Solve frac{sqrt{17}-sqrt{18}}{sqrt{2}*sqrt{5}}

$$\frac { \sqrt { 17 } - \sqrt { 18 } } { \sqrt { 2 } \times \sqrt { 5 } }$$

Evaluate

$$\frac{\sqrt{170}-6\sqrt{5}}{10}\approx -0.037800305$$

Solution Steps

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}.

$$\frac{\sqrt{17}-3\sqrt{2}}{\sqrt{2}\sqrt{5}}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{17}-3\sqrt{2}}{\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{17}-3\sqrt{2}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\left(\sqrt{17}-3\sqrt{2}\right)\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\left(\sqrt{17}-3\sqrt{2}\right)\sqrt{10}}{10}$$

Use the distributive property to multiply \sqrt{17}-3\sqrt{2} by \sqrt{10}.

$$\frac{\sqrt{17}\sqrt{10}-3\sqrt{2}\sqrt{10}}{10}$$

To multiply \sqrt{17} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{170}-3\sqrt{2}\sqrt{10}}{10}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\frac{\sqrt{170}-3\sqrt{2}\sqrt{2}\sqrt{5}}{10}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\sqrt{170}-3\times 2\sqrt{5}}{10}$$

Multiply -3 and 2 to get -6.

$$\frac{\sqrt{170}-6\sqrt{5}}{10}$$