Solve -2sqrt{20}+2sqrt{18}-2sqrt{5}

$$- 2 \sqrt { 20 } + 2 \sqrt { 18 } - 2 \sqrt { 5 }$$

Evaluate

$$6\left(\sqrt{2}-\sqrt{5}\right)\approx -4.931126491$$

Solution Steps

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}.

$$-2\times 2\sqrt{5}+2\sqrt{18}-2\sqrt{5}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{5}+2\sqrt{18}-2\sqrt{5}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Multiply 2 and 3 to get 6.

$$-4\sqrt{5}+6\sqrt{2}-2\sqrt{5}$$

Combine -4\sqrt{5} and -2\sqrt{5} to get -6\sqrt{5}.

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

Factor

$$6 {(\sqrt{2} - \sqrt{5})} = -4.931126491$$