Solve sqrt{3}*sqrt{6}-sqrt{50}

$$\sqrt { 3 } \times \sqrt { 6 } - \sqrt { 50 }$$

Evaluate

$$-2\sqrt{2}\approx -2.828427125$$

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}.

$$\sqrt{3}\sqrt{3}\sqrt{2}-\sqrt{50}$$

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

$$3\sqrt{2}-\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$3\sqrt{2}-5\sqrt{2}$$

Combine 3\sqrt{2} and -5\sqrt{2} to get -2\sqrt{2}.

$$-2\sqrt{2}$$