Solve 3sqrt{5}-2sqrt{12}-2sqrt{75}-5sqrt{20}

$$3 \sqrt { 5 } - 2 \sqrt { 12 } - 2 \sqrt { 75 } - 5 \sqrt { 20 }$$

Evaluate

$$-7\sqrt{5}-14\sqrt{3}\approx -39.901187148$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$3\sqrt{5}-2\times 2\sqrt{3}-2\sqrt{75}-5\sqrt{20}$$

Multiply -2 and 2 to get -4.

$$3\sqrt{5}-4\sqrt{3}-2\sqrt{75}-5\sqrt{20}$$

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}.

$$3\sqrt{5}-4\sqrt{3}-2\times 5\sqrt{3}-5\sqrt{20}$$

Multiply -2 and 5 to get -10.

$$3\sqrt{5}-4\sqrt{3}-10\sqrt{3}-5\sqrt{20}$$

Combine -4\sqrt{3} and -10\sqrt{3} to get -14\sqrt{3}.

$$3\sqrt{5}-14\sqrt{3}-5\sqrt{20}$$

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}.

$$3\sqrt{5}-14\sqrt{3}-5\times 2\sqrt{5}$$

Multiply -5 and 2 to get -10.

$$3\sqrt{5}-14\sqrt{3}-10\sqrt{5}$$

Combine 3\sqrt{5} and -10\sqrt{5} to get -7\sqrt{5}.

$$-7\sqrt{5}-14\sqrt{3}$$