Solve frac{-5sqrt{8^2+4}}{8^2}

$$\frac { - 5 \sqrt { 8 ^ { 2 } + 4 } } { 8 ^ { 2 } }$$

Evaluate

$$-\frac{5\sqrt{17}}{32}\approx -0.644235254$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\frac{-5\sqrt{64+4}}{8^{2}}$$

Add 64 and 4 to get 68.

$$\frac{-5\sqrt{68}}{8^{2}}$$

Factor 68=2^{2}\times 17. Rewrite the square root of the product \sqrt{2^{2}\times 17} as the product of square roots \sqrt{2^{2}}\sqrt{17}. Take the square root of 2^{2}.

$$\frac{-5\times 2\sqrt{17}}{8^{2}}$$

Multiply -5 and 2 to get -10.

$$\frac{-10\sqrt{17}}{8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{-10\sqrt{17}}{64}$$

Divide -10\sqrt{17} by 64 to get -\frac{5}{32}\sqrt{17}.

$$-\frac{5}{32}\sqrt{17}$$