Solve sqrt{275}-sqrt{99}

$$\sqrt { 275 } - \sqrt { 99 }$$

Evaluate

$$2\sqrt{11}\approx 6.633249581$$

Solution Steps

Factor 275=5^{2}\times 11. Rewrite the square root of the product \sqrt{5^{2}\times 11} as the product of square roots \sqrt{5^{2}}\sqrt{11}. Take the square root of 5^{2}.

$$5\sqrt{11}-\sqrt{99}$$

Factor 99=3^{2}\times 11. Rewrite the square root of the product \sqrt{3^{2}\times 11} as the product of square roots \sqrt{3^{2}}\sqrt{11}. Take the square root of 3^{2}.

$$5\sqrt{11}-3\sqrt{11}$$

Combine 5\sqrt{11} and -3\sqrt{11} to get 2\sqrt{11}.

$$2\sqrt{11}$$