Solve sqrt{28}+sqrt{18}+4sqrt{2}+sqrt{112}

$$\sqrt { 28 } + \sqrt { 18 } + 4 \sqrt { 2 } + \sqrt { 112 }$$

Evaluate

$$\sqrt{7}\left(\sqrt{14}+6\right)\approx 25.774002803$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{7}+\sqrt{18}+4\sqrt{2}+\sqrt{112}$$

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}.

$$2\sqrt{7}+3\sqrt{2}+4\sqrt{2}+\sqrt{112}$$

Combine 3\sqrt{2} and 4\sqrt{2} to get 7\sqrt{2}.

$$2\sqrt{7}+7\sqrt{2}+\sqrt{112}$$

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$2\sqrt{7}+7\sqrt{2}+4\sqrt{7}$$

Combine 2\sqrt{7} and 4\sqrt{7} to get 6\sqrt{7}.

$$6\sqrt{7}+7\sqrt{2}$$