Solve sqrt{18}+sqrt{98}-sqrt{27}

$$\sqrt{ 18 } + \sqrt{ 98 } - \sqrt{ 27 }$$

Evaluate

$$10\sqrt{2}-3\sqrt{3}\approx 8.945983201$$

Solution Steps

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}.

$$3\sqrt{2}+\sqrt{98}-\sqrt{27}$$

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}.

$$3\sqrt{2}+7\sqrt{2}-\sqrt{27}$$

Combine 3\sqrt{2} and 7\sqrt{2} to get 10\sqrt{2}.

$$10\sqrt{2}-\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$10\sqrt{2}-3\sqrt{3}$$