THE TIGER WHO EATS SQUARE ROOTS


Imagine that we are stranded on a desert island with nothing to help us but our wits, and there is a hungry Tiger just down the beach. You happen to know that the Tiger has very peculiar dietary habits: He only eats square roots. And if he can't find square roots, he becomes angry and carnivorous. When the Tiger orders up a particular square root, he wants a decimal answer and he wants it to be accurate!

There is the tiger and ...
Today, the Tiger has developed a taste for square roots of numbers near 100. Now, the square root of 100 is 10, so it would be nice if we could just hand him a ten every few minutes. Or better yet, just toss him a pile of 10s and be done with it. Unfortunately, when the Tiger demands the square root of 99, he's not satisfied with 10 as the answer; the tiger is feeling grumpy and it's just not close enough. What to do? Answer with a 9? Nine and a half? 9.9? 9.25496?

... he likes square roots.None of these guesses are close enough and the Tiger's getting angry and hungry. Too bad we don't have a calculator or a table of square roots! But this is a desert island and we were lucky to get here at all.

We need a method for supplying square roots on demand.

Our role in dealing with the Tiger is to act like the square root function! Here are some things to consider.

Question 1. What is a square root?[What?]
Question 2. Is the square root of 99 really less than the square root of 100?[Less Than?]
Question 3. Is the square root of 99 really close to the square root of 100?
And how close is "close" anyway?
[Close To?]


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William A. Bogley
Robby Robson