Solve frac{10sqrt{2}}{sqrt{3}}*frac{sqrt{3}}{sqrt{3}}

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

Evaluate

$$\frac{10\sqrt{6}}{3}\approx 8.164965809$$

Solution Steps

Divide \sqrt{3} by \sqrt{3} to get 1.

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

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

$$\frac{10\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times 1$$

The square of \sqrt{3} is 3.

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

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

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

Express \frac{10\sqrt{6}}{3}\times 1 as a single fraction.

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