Solve frac{sqrt{14}}{3sqrt{35}}

$$\frac { \sqrt { 14 } } { 3 \sqrt { 35 } }$$

Evaluate

$$\frac{\sqrt{10}}{15}\approx 0.210818511$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{14}}{3\sqrt{35}} by multiplying numerator and denominator by \sqrt{35}.

$$\frac{\sqrt{14}\sqrt{35}}{3\left(\sqrt{35}\right)^{2}}$$

The square of \sqrt{35} is 35.

$$\frac{\sqrt{14}\sqrt{35}}{3\times 35}$$

To multiply \sqrt{14} and \sqrt{35}, multiply the numbers under the square root.

$$\frac{\sqrt{490}}{3\times 35}$$

Multiply 3 and 35 to get 105.

$$\frac{\sqrt{490}}{105}$$

Factor 490=7^{2}\times 10. Rewrite the square root of the product \sqrt{7^{2}\times 10} as the product of square roots \sqrt{7^{2}}\sqrt{10}. Take the square root of 7^{2}.

$$\frac{7\sqrt{10}}{105}$$

Divide 7\sqrt{10} by 105 to get \frac{1}{15}\sqrt{10}.

$$\frac{1}{15}\sqrt{10}$$