# Square Root Surprise

## X + √(2) - (√(2) - 1) = X + 1

__Examples:__

-3 + √(2) - (√(2) - 1) = -2

1 + √(2) - (√(2) - 1) = 2

3 + √(2) - (√(2) - 1) = 4

½ + √(2) - (√(2) - 1) = 1 + ½

√(3) + √(2) - (√(2) - 1) = √(3) + 1

0 + √(2) - (√(2) - 1) = 1

Miss Zero Digit representing the number **zero(0)** again!

You can also plug an imaginary or complex number into **X**!

*i* + √(2) - (√(2) - 1) = 1 + *i*

-*i* + √(2) - (√(2) - 1) = 1 - *i*

(1 + *i*) + √(2) - (√(2) - 1) = 2 + *i*

(1 - *i*) + √(2) - (√(2) - 1) = 2 - *i*

(-2 + *i*) + √(2) - (√(2) - 1) = -1 + *i*

(-2 - *i*) + √(2) - (√(2) - 1) = -1 - *i*

What I just noticed with the complex numbers is that if the *independent* complex number has a *plus* between the *real & imaginary values*, then so will the *dependent* complex number! (The independent one is to the left of the equal sign.) That goes double for a *minus!*

## None of these examples look like they're correct, do they? But here's why all of this is true:

The binomial in parentheses: **(√(2) - 1)** is the difference between *the square root of* 2 & 1. Adding the difference between two numbers to the smaller one will always give you the bigger one as the sum! Surprise!

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© Derek Cumberbatch