Solve sqrt{30}div3sqrt{13/5}

$$\sqrt { 30 } \div 3 \sqrt { 1 \frac { 3 } { 5 } }$$

Evaluate

$$\frac{4\sqrt{3}}{3}\approx 2.309401077$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\sqrt{30}}{3}\sqrt{\frac{5+3}{5}}$$

Add 5 and 3 to get 8.

$$\frac{\sqrt{30}}{3}\sqrt{\frac{8}{5}}$$

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

$$\frac{\sqrt{30}}{3}\times \frac{\sqrt{8}}{\sqrt{5}}$$

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}.

$$\frac{\sqrt{30}}{3}\times \frac{2\sqrt{2}}{\sqrt{5}}$$

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

$$\frac{\sqrt{30}}{3}\times \frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{30}}{3}\times \frac{2\sqrt{2}\sqrt{5}}{5}$$

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

$$\frac{\sqrt{30}}{3}\times \frac{2\sqrt{10}}{5}$$

Multiply \frac{\sqrt{30}}{3} times \frac{2\sqrt{10}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{30}\times 2\sqrt{10}}{3\times 5}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

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

Multiply \sqrt{10} and \sqrt{10} to get 10.

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

Multiply 10 and 2 to get 20.

$$\frac{20\sqrt{3}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{20\sqrt{3}}{15}$$

Divide 20\sqrt{3} by 15 to get \frac{4}{3}\sqrt{3}.

$$\frac{4}{3}\sqrt{3}$$