Solve sqrt{2}(3-sqrt{3})-sqrt{8}

$$\sqrt{ 2 } (3- \sqrt{ 3 } )- \sqrt{ 8 }$$

Evaluate

$$\sqrt{2}-\sqrt{6}\approx -1.03527618$$

Solution Steps

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

$$3\sqrt{2}-\sqrt{2}\sqrt{3}-\sqrt{8}$$

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

$$3\sqrt{2}-\sqrt{6}-\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Combine 3\sqrt{2} and -2\sqrt{2} to get \sqrt{2}.

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