Solve sqrt{3}*sqrt{6}-sqrt{8}

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

Evaluate

$$\sqrt{2}\approx 1.414213562$$

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}.

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

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

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

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}.

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

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

$$\sqrt{2}$$