Solve 5sqrt{98}+sqrt{72}

$$5 \sqrt { 98 } + \sqrt { 72 }$$

Evaluate

$$41\sqrt{2}\approx 57.982756057$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$5\times 7\sqrt{2}+\sqrt{72}$$

Multiply 5 and 7 to get 35.

$$35\sqrt{2}+\sqrt{72}$$

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}.

$$35\sqrt{2}+6\sqrt{2}$$

Combine 35\sqrt{2} and 6\sqrt{2} to get 41\sqrt{2}.

$$41\sqrt{2}$$