Solve sqrt{35}divsqrt{13/5}

$$\sqrt { 35 } \div \sqrt { 1 \frac { 3 } { 5 } }$$

Evaluate

$$\frac{5\sqrt{14}}{4}\approx 4.677071733$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\sqrt{35}}{\sqrt{\frac{5+3}{5}}}$$

Add 5 and 3 to get 8.

$$\frac{\sqrt{35}}{\sqrt{\frac{8}{5}}}$$

Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\sqrt{35}}{\frac{\sqrt{8}}{\sqrt{5}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\sqrt{35}}{\frac{2\sqrt{2}}{\sqrt{5}}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{35}}{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{35}}{\frac{2\sqrt{2}\sqrt{5}}{5}}$$

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

$$\frac{\sqrt{35}}{\frac{2\sqrt{10}}{5}}$$

Divide \sqrt{35} by \frac{2\sqrt{10}}{5} by multiplying \sqrt{35} by the reciprocal of \frac{2\sqrt{10}}{5}.

$$\frac{\sqrt{35}\times 5}{2\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{35}\times 5}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{35}\times 5\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{35}\times 5\sqrt{10}}{2\times 10}$$

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

$$\frac{\sqrt{350}\times 5}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{\sqrt{350}\times 5}{20}$$

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}.

$$\frac{5\sqrt{14}\times 5}{20}$$

Multiply 5 and 5 to get 25.

$$\frac{25\sqrt{14}}{20}$$

Divide 25\sqrt{14} by 20 to get \frac{5}{4}\sqrt{14}.

$$\frac{5}{4}\sqrt{14}$$