Solve sqrt{7}+sqrt{75}-2(sqrt{7}-sqrt{12})

$$\sqrt { 7 } + \sqrt { 75 } - 2 ( \sqrt { 7 } - \sqrt { 12 } )$$

Evaluate

$$9\sqrt{3}-\sqrt{7}\approx 12.942705957$$

Solution Steps

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}.

$$\sqrt{7}+5\sqrt{3}-2\left(\sqrt{7}-\sqrt{12}\right)$$

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}.

$$\sqrt{7}+5\sqrt{3}-2\left(\sqrt{7}-2\sqrt{3}\right)$$

Use the distributive property to multiply -2 by \sqrt{7}-2\sqrt{3}.

$$\sqrt{7}+5\sqrt{3}-2\sqrt{7}+4\sqrt{3}$$

Combine \sqrt{7} and -2\sqrt{7} to get -\sqrt{7}.

$$-\sqrt{7}+5\sqrt{3}+4\sqrt{3}$$

Combine 5\sqrt{3} and 4\sqrt{3} to get 9\sqrt{3}.

$$-\sqrt{7}+9\sqrt{3}$$