Solve sqrt{12}-sqrt{27}-sqrt{45}+sqrt{50}

$$\sqrt { 12 } - \sqrt { 27 } - \sqrt { 45 } + \sqrt { 50 }$$

Evaluate

$$5\sqrt{2}-\sqrt{3}-3\sqrt{5}\approx -1.369186928$$

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}.

$$2\sqrt{3}-\sqrt{27}-\sqrt{45}+\sqrt{50}$$

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}.

$$2\sqrt{3}-3\sqrt{3}-\sqrt{45}+\sqrt{50}$$

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

$$-\sqrt{3}-\sqrt{45}+\sqrt{50}$$

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}.

$$-\sqrt{3}-3\sqrt{5}+\sqrt{50}$$

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}.

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