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In mathematics, the general root, or the n^th root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:

ⁿ√a = b
bⁿ = a

Estimating a Root

1. Pick a provisional value b.
2. Divide a by b. If the resulting c already matches the required precision, you’re done.
3. Combine b and c by taking their average; treat this as the next guess.
4. Go back to step two and iterate.

EX:	Find √27 to 3 decimal places
	Guess: 5.125 27 ÷ 5.125 = 5.268 (5.125 + 5.268)/2 = 5.197 27 ÷ 5.197 = 5.195 (5.195 + 5.197)/2 = 5.196 27 ÷ 5.196 = 5.196

Estimating an n^th Root

1. Choose an initial guess b.
2. Compute a divided by b^n-1. If the quotient c meets the desired accuracy, stop.
3. Form a new estimate by averaging: (b × (n-1) + c) / n.
4. Return to step two and iterate.

EX:	Find 8√15 to 3 decimal places
	Guess: 1.432 15 ÷ 1.4327 = 1.405 (1.432 × 7 + 1.405)/8 = 1.388 15 ÷ 1.3887 = 1.403 (1.403 × 7 + 1.388)/8 = 1.402

It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places.

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