Solve -2sqrt{45}-3sqrt{20}-2sqrt{6}

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

Evaluate

$$-2\sqrt{6}-12\sqrt{5}\approx -31.731795216$$

Solution Steps

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}.

$$-2\times 3\sqrt{5}-3\sqrt{20}-2\sqrt{6}$$

Multiply -2 and 3 to get -6.

$$-6\sqrt{5}-3\sqrt{20}-2\sqrt{6}$$

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}.

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

Multiply -3 and 2 to get -6.

$$-6\sqrt{5}-6\sqrt{5}-2\sqrt{6}$$

Combine -6\sqrt{5} and -6\sqrt{5} to get -12\sqrt{5}.

$$-12\sqrt{5}-2\sqrt{6}$$