Solve sqrt{50}+7sqrt{18}-3sqrt{2}

$$\sqrt { 50 } + 7 \sqrt { 18 } - 3 \sqrt { 2 }$$

Evaluate

$$23\sqrt{2}\approx 32.526911935$$

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}.

$$5\sqrt{2}+7\sqrt{18}-3\sqrt{2}$$

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}.

$$5\sqrt{2}+7\times 3\sqrt{2}-3\sqrt{2}$$

Multiply 7 and 3 to get 21.

$$5\sqrt{2}+21\sqrt{2}-3\sqrt{2}$$

Combine 5\sqrt{2} and 21\sqrt{2} to get 26\sqrt{2}.

$$26\sqrt{2}-3\sqrt{2}$$

Combine 26\sqrt{2} and -3\sqrt{2} to get 23\sqrt{2}.

$$23\sqrt{2}$$