Solve sqrt{50}+2sqrt{72}-3sqrt{2}=

$$\sqrt { 50 } + 2 \sqrt { 72 } - 3 \sqrt { 2 } =$$

Evaluate

$$14\sqrt{2}\approx 19.798989873$$

Solution Steps

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}.

$$5\sqrt{2}+2\sqrt{72}-3\sqrt{2}$$

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}.

$$5\sqrt{2}+2\times 6\sqrt{2}-3\sqrt{2}$$

Multiply 2 and 6 to get 12.

$$5\sqrt{2}+12\sqrt{2}-3\sqrt{2}$$

Combine 5\sqrt{2} and 12\sqrt{2} to get 17\sqrt{2}.

$$17\sqrt{2}-3\sqrt{2}$$

Combine 17\sqrt{2} and -3\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}$$