Solve sqrt{27}-sqrt{50}+sqrt{12}+sqrt{8}

$$\sqrt { 27 } - \sqrt { 50 } + \sqrt { 12 } + \sqrt { 8 }$$

Evaluate

$$5\sqrt{3}-3\sqrt{2}\approx 4.417613351$$

Solution Steps

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}.

$$3\sqrt{3}-\sqrt{50}+\sqrt{12}+\sqrt{8}$$

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}.

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

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}.

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

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

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

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}.

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

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

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