Solve 2sqrt{12}divsqrt{50}1/2sqrt{3/4}

$$2 \sqrt{ 12 } \div \sqrt{ 50 } \frac{ 1 }{ 2 } \sqrt{ \frac{ 3 }{ 4 } }$$

Evaluate

$$\frac{3\sqrt{2}}{10}\approx 0.424264069$$

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}.

$$\frac{2\times 2\sqrt{3}}{\sqrt{50}}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}}{\sqrt{50}}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{4\sqrt{3}}{5\sqrt{2}}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

Rationalize the denominator of \frac{4\sqrt{3}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

The square of \sqrt{2} is 2.

$$\frac{4\sqrt{3}\sqrt{2}}{5\times 2}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{4\sqrt{6}}{5\times 2}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

Multiply 5 and 2 to get 10.

$$\frac{4\sqrt{6}}{10}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

Divide 4\sqrt{6} by 10 to get \frac{2}{5}\sqrt{6}.

$$\frac{2}{5}\sqrt{6}\times \frac{1}{2}\sqrt{\frac{3}{4}}$$

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{5\times 2}\sqrt{6}\sqrt{\frac{3}{4}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{5}\sqrt{6}\sqrt{\frac{3}{4}}$$

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

$$\frac{1}{5}\sqrt{6}\times \frac{\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{1}{5}\sqrt{6}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{1}{5} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{3}}{5\times 2}\sqrt{6}$$

Multiply 5 and 2 to get 10.

$$\frac{\sqrt{3}}{10}\sqrt{6}$$

Express \frac{\sqrt{3}}{10}\sqrt{6} as a single fraction.

$$\frac{\sqrt{3}\sqrt{6}}{10}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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