Question

what is the least number greater then 17 but less than 18 which has rational square root​

Answer 1

Pick any nonempty interval and there’s an infinitude of such numbers. You can hit upon the simplest one by trying simple fractions such as 4/1 and 5/1 to start with (one’s too small, the other’s too big), and adding numerators & denominators to get 9/2 (too big), then 13/3 (still too big), eventually arriving at 21/5 which is the simplest answer and the same as the other answer suggests. Also, form the calculator we can do-

√17<4.124  and 18−−√>4.242, so just pick any rational number between 4.124 and 4.242 and square it you will get what you want.

If you hesitate to use a calculator, you can just times 100 with 17 and 18 and get the rough integer value of square root by hand.

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