Solve 2sqrt{18}-5sqrt{8}+sqrt{50}

$$2 \sqrt { 18 } - 5 \sqrt { 8 } + \sqrt { 50 }$$

Evaluate

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

Solution Steps

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}.

$$2\times 3\sqrt{2}-5\sqrt{8}+\sqrt{50}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-5\sqrt{8}+\sqrt{50}$$

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}.

$$6\sqrt{2}-5\times 2\sqrt{2}+\sqrt{50}$$

Multiply -5 and 2 to get -10.

$$6\sqrt{2}-10\sqrt{2}+\sqrt{50}$$

Combine 6\sqrt{2} and -10\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}+\sqrt{50}$$

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}.

$$-4\sqrt{2}+5\sqrt{2}$$

Combine -4\sqrt{2} and 5\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}$$