Solve frac{4(7sqrt{7}+2sqrt{5}-3sqrt{7})}{sqrt{2}(sqrt{8}-sqrt{2})}

$$\frac { 4 ( 7 \sqrt { 7 } + 2 \sqrt { 5 } - 3 \sqrt { 7 } ) } { \sqrt { 2 } ( \sqrt { 8 } - \sqrt { 2 } ) }$$

Evaluate

$$4\left(\sqrt{5}+2\sqrt{7}\right)\approx 30.110282399$$

Solution Steps

Combine 7\sqrt{7} and -3\sqrt{7} to get 4\sqrt{7}.

$$\frac{4\left(4\sqrt{7}+2\sqrt{5}\right)}{\sqrt{2}\left(\sqrt{8}-\sqrt{2}\right)}$$

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}.

$$\frac{4\left(4\sqrt{7}+2\sqrt{5}\right)}{\sqrt{2}\left(2\sqrt{2}-\sqrt{2}\right)}$$

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

$$\frac{4\left(4\sqrt{7}+2\sqrt{5}\right)}{\sqrt{2}\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{4\left(4\sqrt{7}+2\sqrt{5}\right)}{2}$$

Divide 4\left(4\sqrt{7}+2\sqrt{5}\right) by 2 to get 2\left(4\sqrt{7}+2\sqrt{5}\right).

$$2\left(4\sqrt{7}+2\sqrt{5}\right)$$

Use the distributive property to multiply 2 by 4\sqrt{7}+2\sqrt{5}.

$$8\sqrt{7}+4\sqrt{5}$$