You don't need an expensive GPS system--be it a watch or hand-held system you can wear around your neck with a lanyard--to measure the distance you've traveled from point A to point B in your kayak. You can make a manual calculation if you are kayaking on open water where the horizon is visible and your GPS runs out of battery power. The calculation requires intermediate level math, but can be accomplished with paper and pen or by memory if you are especially good with crunching numbers in your head.
Tips & Warnings
Determine which two perfect squares your square falls between. For example, the square root of 12 will fall between the square root of 9 (3 times 2 equals 9) and the square root of 16 (4 times 4 equals 16). Divide your square by one of these two square roots. For example, divide 12 by 3 to get a total of 4. Take the above answer (4) and average it with the root by which you chose to divide your square: 3. Therefore, 4 plus 3/2 = 3.5, which means the square root of 12 is 3.5.