Solve sqrt{28}-sqrt{27}+sqrt{63}-sqrt{12}

$$\sqrt{ 28 } - \sqrt{ 27 } + \sqrt{ 63 } - \sqrt{ 12 }$$

Evaluate

$$5\left(\sqrt{7}-\sqrt{3}\right)\approx 4.568502517$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{7}-\sqrt{27}+\sqrt{63}-\sqrt{12}$$

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}.

$$2\sqrt{7}-3\sqrt{3}+\sqrt{63}-\sqrt{12}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$2\sqrt{7}-3\sqrt{3}+3\sqrt{7}-\sqrt{12}$$

Combine 2\sqrt{7} and 3\sqrt{7} to get 5\sqrt{7}.

$$5\sqrt{7}-3\sqrt{3}-\sqrt{12}$$

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}.

$$5\sqrt{7}-3\sqrt{3}-2\sqrt{3}$$

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

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