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A rational number is a number that can be expressed as a quotient a/b of two integers.

Let us Guess the number step by step:

1) The number lies between 1 and 10

So, the chances are all the 10 numbers

2) its square is rational and lies between 1 and 10

so, the chances are high if we go with medium (1+10)/2=11/2

3) The number is larger than pi=3.14

11/2=5.50-> we prove that 11/2>pi

so, the guessing number is 11/2

[QUOTE="MathLover1, post: 1101640, member: 280"] A rational number is a number that can be expressed as a quotient a/b of two integers. Let us Guess the number step by step: 1) The number lies between 1 and 10 So, the chances are all the 10 numbers 2) its square is [B]rational [/B]and lies between 1 and 10 so, the chances are high if we go with [B]medium[/B] (1+10)/2=[B]11/2[/B] 3) The number is larger than [B]pi=3.14[/B] [B]11/2=5.50-> we prove that [B]11/2>pi[/B][/B] so, the guessing number is [B]11/2[/B] [/QUOTE]