Originally Posted by

**pacman** if x is the side of the square with area 1, now if we increase it with y and area 2, we have

(x + y)(x + y) = 2,

x^2 + 2xy + y^2 = 2

but x^2 = 1 and x = 1, we have

1 + 2(1)(y) + y^2 = 2, re-arranging

1 - 2 + 2y + y^2 = 0

y^2 + 2y - 1 = 0,

Use quadratic formula:

y1 = sqrt 2 - 1

y2 = - sqrt 2 - 1

Notice that y1 is the only positive, so y = sqrt 2 - 1

length of the the new square = x + y = 1 + (sqrt 2 - 1) = sqrt 2.

If your square with side square root of 2, that is irrational . . . . hard to measure, right?

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NOTE: In general, doubling the area of ANY square with a side of length x, multiply it with sqrt 2, the SQUARE that,

New Area = [(x)(sqrt 2)]^2