Solve 3sqrt{99}+4sqrt{250}

$$3 \sqrt { 99 } + 4 \sqrt { 250 }$$

Evaluate

$$9\sqrt{11}+20\sqrt{10}\approx 93.095176317$$

Solution Steps

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}.

$$3\times 3\sqrt{11}+4\sqrt{250}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{11}+4\sqrt{250}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$9\sqrt{11}+4\times 5\sqrt{10}$$

Multiply 4 and 5 to get 20.

$$9\sqrt{11}+20\sqrt{10}$$