Solve (1-sqrt{2})^0+(1/2)^-1-sqrt{8}divsqrt{2}+1sqrt{2}-21

$$( 1 - \sqrt { 2 } ) ^ { 0 } + ( \frac { 1 } { 2 } ) ^ { - 1 } - \sqrt { 8 } \div \sqrt { 2 } + 1 \sqrt { 2 } - 21$$

Evaluate

$$\sqrt{2}-20\approx -18.585786438$$

Solution Steps

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

$$1+\left(\frac{1}{2}\right)^{-1}-\frac{\sqrt{8}}{\sqrt{2}}+1\sqrt{2}-21$$

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

$$1+2-\frac{\sqrt{8}}{\sqrt{2}}+1\sqrt{2}-21$$

Add 1 and 2 to get 3.

$$3-\frac{\sqrt{8}}{\sqrt{2}}+1\sqrt{2}-21$$

Rewrite the division of square roots \frac{\sqrt{8}}{\sqrt{2}} as the square root of the division \sqrt{\frac{8}{2}} and perform the division.

$$3-\sqrt{4}+1\sqrt{2}-21$$

Calculate the square root of 4 and get 2.

$$3-2+1\sqrt{2}-21$$

Subtract 2 from 3 to get 1.

$$1+1\sqrt{2}-21$$

Subtract 21 from 1 to get -20.

$$-20+1\sqrt{2}$$

For any term t, t\times 1=t and 1t=t.

$$-20+\sqrt{2}$$