Solve frac{sqrt{6}sqrt{3}-sqrt{6}sqrt{2}}{1}-4/1

$$\frac { \sqrt { 6 } \sqrt { 3 } - \sqrt { 6 } \sqrt { 2 } } { 1 } - \frac { 4 } { 1 }$$

Evaluate

$$3\sqrt{2}-2\sqrt{3}-4\approx -3.221460928$$

Solution Steps

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}.

$$\frac{\sqrt{3}\sqrt{2}\sqrt{3}-\sqrt{6}\sqrt{2}}{1}-\frac{4}{1}$$

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

$$\frac{3\sqrt{2}-\sqrt{6}\sqrt{2}}{1}-\frac{4}{1}$$

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}.

$$\frac{3\sqrt{2}-\sqrt{2}\sqrt{3}\sqrt{2}}{1}-\frac{4}{1}$$

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

$$\frac{3\sqrt{2}-2\sqrt{3}}{1}-\frac{4}{1}$$

Anything divided by one gives itself.

$$3\sqrt{2}-2\sqrt{3}-\frac{4}{1}$$

Anything divided by one gives itself.

$$3\sqrt{2}-2\sqrt{3}-4$$