Solve sqrt{288}-sqrt{162}+sqrt{98}

$$\sqrt{ 288 } - \sqrt{ 162 } + \sqrt{ 98 }$$

Evaluate

$$10\sqrt{2}\approx 14.142135624$$

Solution Steps

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$12\sqrt{2}-\sqrt{162}+\sqrt{98}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$12\sqrt{2}-9\sqrt{2}+\sqrt{98}$$

Combine 12\sqrt{2} and -9\sqrt{2} to get 3\sqrt{2}.

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

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}.

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

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

$$10\sqrt{2}$$