Chapter A.1, Problem 150AYU

To determine

To find: Number game I’m thinking of a number! It lies between 1 and 10; its square is rational and lies between 1 and 10. The number is larger than $\pi$. Correct to two decimal places (that is, truncated to two decimal places), name the number. Now think of your own number, describe it, and challenge a fellow student to name it.

Answer to Problem 150AYU

$3.15$ and $3.16$.

Explanation of Solution

$\pi \approx 3.14$

The number greater than $\pi$ and satisfies the condition is that its square is rational and lies between 1 and 10.

Therefore the numbers are $3.15$ and $3.16$.