Solve 2sqrt{44}+sqrt{99}-5sqrt{17}+5sqrt{11}

$$2 \sqrt{ 44 } + \sqrt{ 99 } -5 \sqrt{ 17 } +5 \sqrt{ 11 }$$

Evaluate

$$12\sqrt{11}-5\sqrt{17}\approx 19.183969356$$

Solution Steps

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$2\times 2\sqrt{11}+\sqrt{99}-5\sqrt{17}+5\sqrt{11}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{11}+\sqrt{99}-5\sqrt{17}+5\sqrt{11}$$

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}.

$$4\sqrt{11}+3\sqrt{11}-5\sqrt{17}+5\sqrt{11}$$

Combine 4\sqrt{11} and 3\sqrt{11} to get 7\sqrt{11}.

$$7\sqrt{11}-5\sqrt{17}+5\sqrt{11}$$

Combine 7\sqrt{11} and 5\sqrt{11} to get 12\sqrt{11}.

$$12\sqrt{11}-5\sqrt{17}$$