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

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

Evaluate

$$\frac{12\sqrt{2}}{5}\approx 3.39411255$$

Solution Steps

To multiply \sqrt{\frac{1}{50}} and \sqrt{\frac{3}{4}}, multiply the numbers under the square root.

$$2\times 2\times 4\sqrt{3}\sqrt{\frac{3}{200}}$$

Multiply 2 and 2 to get 4.

$$4\times 4\sqrt{3}\sqrt{\frac{3}{200}}$$

Multiply 4 and 4 to get 16.

$$16\sqrt{3}\sqrt{\frac{3}{200}}$$

Rewrite the square root of the division \sqrt{\frac{3}{200}} as the division of square roots \frac{\sqrt{3}}{\sqrt{200}}.

$$16\sqrt{3}\times \frac{\sqrt{3}}{\sqrt{200}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$16\sqrt{3}\times \frac{\sqrt{3}}{10\sqrt{2}}$$

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

$$16\sqrt{3}\times \frac{\sqrt{3}\sqrt{2}}{10\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$16\sqrt{3}\times \frac{\sqrt{3}\sqrt{2}}{10\times 2}$$

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

$$16\sqrt{3}\times \frac{\sqrt{6}}{10\times 2}$$

Multiply 10 and 2 to get 20.

$$16\sqrt{3}\times \frac{\sqrt{6}}{20}$$

Express 16\times \frac{\sqrt{6}}{20} as a single fraction.

$$\frac{16\sqrt{6}}{20}\sqrt{3}$$

Divide 16\sqrt{6} by 20 to get \frac{4}{5}\sqrt{6}.

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

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}.

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

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

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

Express \frac{4}{5}\times 3 as a single fraction.

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

Multiply 4 and 3 to get 12.

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