Solve sqrt{20}+3sqrt{5}-3sqrt{45}-2sqrt{75}=

$$\sqrt { 20 } + 3 \sqrt { 5 } - 3 \sqrt { 45 } - 2 \sqrt { 75 } =$$

Evaluate

$$-4\sqrt{5}-10\sqrt{3}\approx -26.264779986$$

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}.

$$2\sqrt{5}+3\sqrt{5}-3\sqrt{45}-2\sqrt{75}$$

Combine 2\sqrt{5} and 3\sqrt{5} to get 5\sqrt{5}.

$$5\sqrt{5}-3\sqrt{45}-2\sqrt{75}$$

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}.

$$5\sqrt{5}-3\times 3\sqrt{5}-2\sqrt{75}$$

Multiply -3 and 3 to get -9.

$$5\sqrt{5}-9\sqrt{5}-2\sqrt{75}$$

Combine 5\sqrt{5} and -9\sqrt{5} to get -4\sqrt{5}.

$$-4\sqrt{5}-2\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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

Multiply -2 and 5 to get -10.

$$-4\sqrt{5}-10\sqrt{3}$$