Solve frac{sqrt{2}*sqrt{6}-3}{sqrt{3}}=

$$\frac { \sqrt { 2 } \times \sqrt { 6 } - 3 } { \sqrt { 3 } } =$$

Evaluate

$$2-\sqrt{3}\approx 0.267949192$$

Solution Steps

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}.

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

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

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

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

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

The square of \sqrt{3} is 3.

$$\frac{\left(2\sqrt{3}-3\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 2\sqrt{3}-3 by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Divide each term of 6-3\sqrt{3} by 3 to get 2-\sqrt{3}.

$$2-\sqrt{3}$$