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Question
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
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Solution
Step 1: Formula
The distance between two points (x1, y1) and (x2, y2) is given by:
`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
Step 2: Substitute values
`x_1 = sqrt3 + 1, y_1 = 1, x_2 = 0, y_2 = sqrt3`
`d = sqrt((0 - (sqrt3 + 1))^2 + (sqrt3 - 1)^2)`
Step 3: Simplify
`d = sqrt((sqrt3 + 1)^2 + (sqrt3 - 1)^2)`
`= sqrt((3 + 2sqrt3 + 1) + (3 - 2sqrt3 + 1))`
`= sqrt((4 + 2sqrt3) + (4 - 2sqrt3))`
`= sqrt8`
Step 4: Simplify further
`d = 2sqrt2`
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