Solve =sqrt{8}-2sin45^circ+(1/2)^-1

$$= \sqrt { 8 } - 2 \sin 45 ^ { \circ } + ( \frac { 1 } { 2 } ) ^ { - 1 }$$

Evaluate

$$\sqrt{2}+2\approx 3.414213562$$

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}.

$$2\sqrt{2}-2\sin(45)+\left(\frac{1}{2}\right)^{-1}$$

Get the value of \sin(45) from trigonometric values table.

$$2\sqrt{2}-2\times \frac{\sqrt{2}}{2}+\left(\frac{1}{2}\right)^{-1}$$

Cancel out 2 and 2.

$$2\sqrt{2}-\sqrt{2}+\left(\frac{1}{2}\right)^{-1}$$

Combine 2\sqrt{2} and -\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}+\left(\frac{1}{2}\right)^{-1}$$

Calculate \frac{1}{2} to the power of -1 and get 2.

$$\sqrt{2}+2$$