Solve frac{5sqrt{6}}{sqrt{3}}*frac{sqrt{3}}{sqrt{3}}

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

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

Solution Steps

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

$$\frac{5\sqrt{6}}{\sqrt{3}}\times 1$$

Rationalize the denominator of \frac{5\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{5\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times 1$$

The square of \sqrt{3} is 3.

$$\frac{5\sqrt{6}\sqrt{3}}{3}\times 1$$

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}.

$$\frac{5\sqrt{3}\sqrt{2}\sqrt{3}}{3}\times 1$$

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

$$\frac{5\times 3\sqrt{2}}{3}\times 1$$

Cancel out 3 and 3.

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

Multiply 5 and 1 to get 5.

$$5\sqrt{2}$$