Solve (1)+(2sqrt{2015})^0+2sin45^circ-sqrt{8}

$$( 1 ) + ( 2 \sqrt { 2015 } ) ^ { 0 } + 2 \sin 45 ^ { \circ } - \sqrt { 8 }$$

Evaluate

$$2-\sqrt{2}\approx 0.585786438$$

Solution Steps

Calculate 2\sqrt{2015} to the power of 0 and get 1.

$$1+1+2\sin(45)-\sqrt{8}$$

Add 1 and 1 to get 2.

$$2+2\sin(45)-\sqrt{8}$$

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

$$2+2\times \frac{\sqrt{2}}{2}-\sqrt{8}$$

Cancel out 2 and 2.

$$2+\sqrt{2}-\sqrt{8}$$

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}.

$$2+\sqrt{2}-2\sqrt{2}$$

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

$$2-\sqrt{2}$$