Solve sqrt{50}-2sqrt{27}-5sqrt{8}+4sqrt{3}-3sqrt{12}=

$$\sqrt { 50 } - 2 \sqrt { 27 } - 5 \sqrt { 8 } + 4 \sqrt { 3 } - 3 \sqrt { 12 } =$$

Evaluate

$$-5\sqrt{2}-8\sqrt{3}\approx -20.927474272$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\sqrt{2}-2\sqrt{27}-5\sqrt{8}+4\sqrt{3}-3\sqrt{12}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$5\sqrt{2}-2\times 3\sqrt{3}-5\sqrt{8}+4\sqrt{3}-3\sqrt{12}$$

Multiply -2 and 3 to get -6.

$$5\sqrt{2}-6\sqrt{3}-5\sqrt{8}+4\sqrt{3}-3\sqrt{12}$$

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}.

$$5\sqrt{2}-6\sqrt{3}-5\times 2\sqrt{2}+4\sqrt{3}-3\sqrt{12}$$

Multiply -5 and 2 to get -10.

$$5\sqrt{2}-6\sqrt{3}-10\sqrt{2}+4\sqrt{3}-3\sqrt{12}$$

Combine 5\sqrt{2} and -10\sqrt{2} to get -5\sqrt{2}.

$$-5\sqrt{2}-6\sqrt{3}+4\sqrt{3}-3\sqrt{12}$$

Combine -6\sqrt{3} and 4\sqrt{3} to get -2\sqrt{3}.

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

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}.

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

Multiply -3 and 2 to get -6.

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

Combine -2\sqrt{3} and -6\sqrt{3} to get -8\sqrt{3}.

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