Solve frac{10*5sqrt{2}}{5sqrt{6}}

$$\frac { 10 \times 5 \sqrt { 2 } } { 5 \sqrt { 6 } }$$

Evaluate

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

Solution Steps

Cancel out 5 in both numerator and denominator.

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

Rationalize the denominator of \frac{10\sqrt{2}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

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}.

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

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

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

Multiply 10 and 2 to get 20.

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

Divide 20\sqrt{3} by 6 to get \frac{10}{3}\sqrt{3}.

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