Solve 32+1/2+sqrt{8}

$$32 + \frac { 1 } { 2 } + \sqrt { 8 }$$

Evaluate

$$2\sqrt{2}+\frac{65}{2}\approx 35.328427125$$

Solution Steps

Convert 32 to fraction \frac{64}{2}.

$$\frac{64}{2}+\frac{1}{2}+\sqrt{8}$$

Since \frac{64}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{64+1}{2}+\sqrt{8}$$

Add 64 and 1 to get 65.

$$\frac{65}{2}+\sqrt{8}$$

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}.

$$\frac{65}{2}+2\sqrt{2}$$

Factor

$$\frac{4 \sqrt{2} + 65}{2} = 35.32842712474619$$