Solve 1/2sqrt{122}+3sqrt{2}+2sqrt{72}=

$$\frac { 1 } { 2 } \sqrt { 122 } + 3 \sqrt { 2 } + 2 \sqrt { 72 } =$$

Evaluate

$$\frac{\sqrt{122}}{2}+15\sqrt{2}\approx 26.735883944$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{1}{2}\sqrt{122}+3\sqrt{2}+2\times 6\sqrt{2}$$

Multiply 2 and 6 to get 12.

$$\frac{1}{2}\sqrt{122}+3\sqrt{2}+12\sqrt{2}$$

Combine 3\sqrt{2} and 12\sqrt{2} to get 15\sqrt{2}.

$$\frac{1}{2}\sqrt{122}+15\sqrt{2}$$

Factor

$$\frac{\sqrt{122} + 30 \sqrt{2}}{2} = 26.735883944190057$$