Solve frac{sqrt{35}}{sqrt{10}}

$$\frac { \sqrt { 35 } } { \sqrt { 10 } }$$

Evaluate

$$\frac{\sqrt{14}}{2}\approx 1.870828693$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{35}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{35}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{35}\sqrt{10}}{10}$$

To multiply \sqrt{35} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{350}}{10}$$

Factor 350=5^{2}\times 14. Rewrite the square root of the product \sqrt{5^{2}\times 14} as the product of square roots \sqrt{5^{2}}\sqrt{14}. Take the square root of 5^{2}.

$$\frac{5\sqrt{14}}{10}$$

Divide 5\sqrt{14} by 10 to get \frac{1}{2}\sqrt{14}.

$$\frac{1}{2}\sqrt{14}$$