Solve sqrt{8}-2sin(45^circ)+1-(1/3)

$$\sqrt{ 8 } -2 \sin ( 45 ^ { \circ } ) +1-( \frac{ 1 }{ 3 } )$$

Evaluate

$$\sqrt{2}+\frac{2}{3}\approx 2.080880229$$

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}.

$$2\sqrt{2}-2\sin(45)+1-\frac{1}{3}$$

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

$$2\sqrt{2}-2\times \frac{\sqrt{2}}{2}+1-\frac{1}{3}$$

Cancel out 2 and 2.

$$2\sqrt{2}-\sqrt{2}+1-\frac{1}{3}$$

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

$$\sqrt{2}+1-\frac{1}{3}$$

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

$$\sqrt{2}+\frac{2}{3}$$