Solve -sqrt{8}-2sqrt{20}-3sqrt{5}

$$- \sqrt{ 8 } -2 \sqrt{ 20 } -3 \sqrt{ 5 }$$

Evaluate

$$-2\sqrt{2}-7\sqrt{5}\approx -18.480902967$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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}.

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

Multiply -2 and 2 to get -4.

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

Combine -4\sqrt{5} and -3\sqrt{5} to get -7\sqrt{5}.

$$-2\sqrt{2}-7\sqrt{5}$$