Solve 2sqrt{2}*5sqrt{1/6}

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

Evaluate

$$\frac{10\sqrt{3}}{3}\approx 5.773502692$$

Solution Steps

Multiply 2 and 5 to get 10.

$$10\sqrt{2}\sqrt{\frac{1}{6}}$$

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$10\sqrt{2}\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

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

$$\frac{10\sqrt{6}}{6}\sqrt{2}$$

Divide 10\sqrt{6} by 6 to get \frac{5}{3}\sqrt{6}.

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

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Express \frac{5}{3}\times 2 as a single fraction.

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

Multiply 5 and 2 to get 10.

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