Question9. Arrange these in order, starting with the smallest. $3^{2}$ $\sqrt{100}$ $4^{2}$ $\sqrt{80}$ $\qquad$ (2)
0. William is thinking of two numbers.
Both numbers are square numbers greater than 1. The sum of the numbers is 100. Write down the two numbers.
12. Ben says "the difference between two consecutive square numbers is always odd." Is Ben correct? You must show your workings.

Studdy Solution
Consider two consecutive square numbers: $n^2$ and $(n+1)^2$. Calculate the difference: $(n+1)^2 - n^2 = n^2 + 2n + 1 - n^2 = 2n + 1$ Since $2n + 1$ is always odd for any integer $n$, Ben is correct.
The arranged order of the expressions is: $\sqrt{80}, 3^2, \sqrt{100}, 4^2$
The two square numbers that sum to 100 are: $36 \text{ and } 64$
Ben's statement is correct. The difference between two consecutive square numbers is always odd.