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

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

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

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}.

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

Cancel out 2 and 2.

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

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}.

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

Cancel out 5 and 5.

$$\sqrt{2}+3\sqrt{2}$$

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

$$4\sqrt{2}$$