Solve 2sqrt{8}+3sqrt{18}-2sqrt{50}

$$2 \sqrt { 8 } + 3 \sqrt { 18 } - 2 \sqrt { 50 }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

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}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{2}+3\sqrt{18}-2\sqrt{50}$$

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}.

$$4\sqrt{2}+3\times 3\sqrt{2}-2\sqrt{50}$$

Multiply 3 and 3 to get 9.

$$4\sqrt{2}+9\sqrt{2}-2\sqrt{50}$$

Combine 4\sqrt{2} and 9\sqrt{2} to get 13\sqrt{2}.

$$13\sqrt{2}-2\sqrt{50}$$

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}.

$$13\sqrt{2}-2\times 5\sqrt{2}$$

Multiply -2 and 5 to get -10.

$$13\sqrt{2}-10\sqrt{2}$$

Combine 13\sqrt{2} and -10\sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}$$