Solve sqrt{288}-sqrt{242}+sqrt{18}

$$\sqrt { 288 } - \sqrt { 242 } + \sqrt { 18 }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

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}.

$$12\sqrt{2}-\sqrt{242}+\sqrt{18}$$

Factor 242=11^{2}\times 2. Rewrite the square root of the product \sqrt{11^{2}\times 2} as the product of square roots \sqrt{11^{2}}\sqrt{2}. Take the square root of 11^{2}.

$$12\sqrt{2}-11\sqrt{2}+\sqrt{18}$$

Combine 12\sqrt{2} and -11\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}+\sqrt{18}$$

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}.

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

Combine \sqrt{2} and 3\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}$$