Solve frac{sqrt{12}}{3sqrt{10}}2sqrt{5}

$$\frac{ \sqrt{ 12 } }{ 3 \sqrt{ 10 } } 2 \sqrt{ 5 }$$

Evaluate

$$\frac{2\sqrt{6}}{3}\approx 1.632993162$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

$$2\times \frac{2\sqrt{3}\sqrt{10}}{3\left(\sqrt{10}\right)^{2}}\sqrt{5}$$

The square of \sqrt{10} is 10.

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

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

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

Multiply 3 and 10 to get 30.

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

Divide 2\sqrt{30} by 30 to get \frac{1}{15}\sqrt{30}.

$$2\times \frac{1}{15}\sqrt{30}\sqrt{5}$$

Multiply 2 and \frac{1}{15} to get \frac{2}{15}.

$$\frac{2}{15}\sqrt{30}\sqrt{5}$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$\frac{2}{15}\sqrt{5}\sqrt{6}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{2}{15}\times 5\sqrt{6}$$

Express \frac{2}{15}\times 5 as a single fraction.

$$\frac{2\times 5}{15}\sqrt{6}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{15}\sqrt{6}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}\sqrt{6}$$