Solve 2sqrt{24}-sqrt{45}-3sqrt{20}

$$2 \sqrt { 24 } - \sqrt { 45 } - 3 \sqrt { 20 }$$

Evaluate

$$4\sqrt{6}-9\sqrt{5}\approx -10.326652826$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\times 2\sqrt{6}-\sqrt{45}-3\sqrt{20}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{6}-\sqrt{45}-3\sqrt{20}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$4\sqrt{6}-3\sqrt{5}-3\sqrt{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$4\sqrt{6}-3\sqrt{5}-3\times 2\sqrt{5}$$

Multiply -3 and 2 to get -6.

$$4\sqrt{6}-3\sqrt{5}-6\sqrt{5}$$

Combine -3\sqrt{5} and -6\sqrt{5} to get -9\sqrt{5}.

$$4\sqrt{6}-9\sqrt{5}$$