Solve 1/2sqrt{8}+3/5sqrt{50}-2/3sqrt{18}

$$\frac { 1 } { 2 } \sqrt { 8 } + \frac { 3 } { 5 } \sqrt { 50 } - \frac { 2 } { 3 } \sqrt { 18 }$$

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}.

$$\frac{1}{2}\times 2\sqrt{2}+\frac{3}{5}\sqrt{50}-\frac{2}{3}\sqrt{18}$$

Cancel out 2 and 2.

$$\sqrt{2}+\frac{3}{5}\sqrt{50}-\frac{2}{3}\sqrt{18}$$

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}.

$$\sqrt{2}+\frac{3}{5}\times 5\sqrt{2}-\frac{2}{3}\sqrt{18}$$

Cancel out 5 and 5.

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

Combine \sqrt{2} and 3\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}-\frac{2}{3}\sqrt{18}$$

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}.

$$4\sqrt{2}-\frac{2}{3}\times 3\sqrt{2}$$

Cancel out 3 and 3.

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

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

$$2\sqrt{2}$$