Solve 4+frac{sqrt{16+8}}{4}

$$4+ \frac{ \sqrt{ 16+8 } }{ 4 }$$

Evaluate

$$\frac{\sqrt{6}}{2}+4\approx 5.224744871$$

Solution Steps

Add 16 and 8 to get 24.

$$4+\frac{\sqrt{24}}{4}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$4+\frac{2\sqrt{6}}{4}$$

Divide 2\sqrt{6} by 4 to get \frac{1}{2}\sqrt{6}.

$$4+\frac{1}{2}\sqrt{6}$$

Factor

$$\frac{\sqrt{6} + 8}{2} = 5.224744871391589$$