Solve sqrt{18}+(sqrt{72}-sqrt{50})

$$\sqrt { 18 } + ( \sqrt { 72 } - \sqrt { 50 } )$$

Evaluate

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

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}.

$$3\sqrt{2}+\sqrt{72}-\sqrt{50}$$

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}.

$$3\sqrt{2}+6\sqrt{2}-\sqrt{50}$$

Combine 3\sqrt{2} and 6\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}-\sqrt{50}$$

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}.

$$9\sqrt{2}-5\sqrt{2}$$

Combine 9\sqrt{2} and -5\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}$$