Solve sqrt{3/16}*sqrt{1/50}*sqrt{48}

$$\sqrt{ \frac{ 3 }{ 16 } } \times \sqrt{ \frac{ 1 }{ 50 } } \times \sqrt{ 48 }$$

Evaluate

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

Solution Steps

To multiply \sqrt{\frac{3}{16}} and \sqrt{\frac{1}{50}}, multiply the numbers under the square root.

$$\sqrt{\frac{3}{800}}\sqrt{48}$$

Rewrite the square root of the division \sqrt{\frac{3}{800}} as the division of square roots \frac{\sqrt{3}}{\sqrt{800}}.

$$\frac{\sqrt{3}}{\sqrt{800}}\sqrt{48}$$

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$\frac{\sqrt{3}}{20\sqrt{2}}\sqrt{48}$$

Rationalize the denominator of \frac{\sqrt{3}}{20\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{20\left(\sqrt{2}\right)^{2}}\sqrt{48}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{20\times 2}\sqrt{48}$$

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

$$\frac{\sqrt{6}}{20\times 2}\sqrt{48}$$

Multiply 20 and 2 to get 40.

$$\frac{\sqrt{6}}{40}\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{\sqrt{6}}{40}\times 4\sqrt{3}$$

Cancel out 40, the greatest common factor in 4 and 40.

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

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

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

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}.

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

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

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