The term "root" has many definitions. To a geocacher, it often refers to plants and anchoring them into the ground. A mathematician will see many meanings; the principal understanding is taking a number and dividing it by a single factor a set amount of times until said factor remains. For example, the publication date of this cache could be seen as the answer to a cube root: 12 multiplied by itself thrice. Another type of root, the square root, is arguably the most well-known and involves only two equal factors.
In order to locate the hidden geocache, complete the following exercises. There is no time limit, and feel free to use whatever resources are needed.
Exercise 1
Calculate where the following equations intersect each other on the x-y grid. Two sets of coordinates will result; retain the pair consisting solely of whole numbers.
![y^2 + (x - 88)^2 = 400 ; 3y + 4x = 448](http://img.geocaching.com/cache/fe9a0c99-e65b-4c85-8616-0a96c44014ae.jpg)
Exercise 2
Solve for a and b.
![a = 1 / x^0.5 ; b = y^0.5 / x](http://img.geocaching.com/cache/6a3b76c4-4c56-4971-8b1d-3ff8dc43e618.jpg)
Exercise 3
Add a to the latitude minutes and b to the longitude minutes.
![N 38 55.555 + a ; W 92 18.971 + b](http://img.geocaching.com/cache/5892b0f1-0d7c-431b-ba4f-2b54fe1e0a3a.jpg)
Pencils down. The answer for exercise number 3 can be found in the back of the book at GeoChecker.
Finding the container itself shouldn't be too difficult. As always, please replace everything as discovered!
Lida Gouchenour of the City of Columbia Parks and Recreation Department provided the permission necessary to make this cache happen!
Capen / Grindstone Series
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