Solve sqrt{8}-3sqrt{18}+sqrt{50}

$$\sqrt{ 8 } -3 \sqrt{ 18 } + \sqrt{ 50 }$$

Evaluate

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

Solution Steps

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}.

$$2\sqrt{2}-3\sqrt{18}+\sqrt{50}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Multiply -3 and 3 to get -9.

$$2\sqrt{2}-9\sqrt{2}+\sqrt{50}$$

Combine 2\sqrt{2} and -9\sqrt{2} to get -7\sqrt{2}.

$$-7\sqrt{2}+\sqrt{50}$$

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}.

$$-7\sqrt{2}+5\sqrt{2}$$

Combine -7\sqrt{2} and 5\sqrt{2} to get -2\sqrt{2}.

$$-2\sqrt{2}$$