Solve sqrt{6}(1-sqrt{2})

$$\sqrt { 6 } ( 1 - \sqrt { 2 } )$$

Evaluate

$$\sqrt{6}-2\sqrt{3}\approx -1.014611872$$

Solution Steps

Use the distributive property to multiply \sqrt{6} by 1-\sqrt{2}.

$$\sqrt{6}-\sqrt{6}\sqrt{2}$$

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}.

$$\sqrt{6}-\sqrt{2}\sqrt{3}\sqrt{2}$$

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

$$\sqrt{6}-2\sqrt{3}$$