Solve 2sqrt{275}+3sqrt{99}

$$2 \sqrt { 275 } + 3 \sqrt { 99 }$$

Evaluate

$$19\sqrt{11}\approx 63.015871017$$

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}.

$$2\times 5\sqrt{11}+3\sqrt{99}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{11}+3\sqrt{99}$$

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}.

$$10\sqrt{11}+3\times 3\sqrt{11}$$

Multiply 3 and 3 to get 9.

$$10\sqrt{11}+9\sqrt{11}$$

Combine 10\sqrt{11} and 9\sqrt{11} to get 19\sqrt{11}.

$$19\sqrt{11}$$