Solve (sqrt{8^2+8^2})div2

$$( \sqrt { 8 ^ { 2 } + 8 ^ { 2 } } ) \div 2$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

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

Calculate 8 to the power of 2 and get 64.

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

Add 64 and 64 to get 128.

$$\frac{\sqrt{128}}{2}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

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

Divide 8\sqrt{2} by 2 to get 4\sqrt{2}.

$$4\sqrt{2}$$