Solve frac{(5+sqrt{8})}{5^2-(sqrt{6})^2}=

$$\frac { ( 5 + \sqrt { 8 } ) } { 5 ^ { 2 } - ( \sqrt { 6 } ) ^ { 2 } } =$$

Evaluate

$$\frac{2\sqrt{2}+5}{19}\approx 0.41202248$$

Solution Steps

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}.

$$\frac{5+2\sqrt{2}}{5^{2}-\left(\sqrt{6}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{5+2\sqrt{2}}{25-\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{5+2\sqrt{2}}{25-6}$$

Subtract 6 from 25 to get 19.

$$\frac{5+2\sqrt{2}}{19}$$