I chose number 24 and 25.
24. The first three triangular numbers are 1, 3 and 6
a) What are the next three triangular numbers?
The next three triangular numbers are 10, 15 and 21.
b) Add together any two consecutive triangular numbers. What do you notice about the sums?
I noticed that the sums are all perfect squares.
25. A square digital photo on the computer has an area of 144cm2.
a) What is the side length of the photo?
The side length is 12cm because the square root of 144 is 12.
b) The photo is enlarged so that the side length is now 36cm. What is the area of the enlarged photo?
The area is now 1296cm2 because 36x36=1296cm2
c) How many times as large as the original is the enlarged area?
The enlarged area is 9 times as large because 144/1296=9 (There is more than method to find this answer, I use division.
d) How many times as large as the original is the enlarged side length?
The enlarged length is 3 times as large because 36/12=3.
e) Use what you know about the square root of a perfect square to identify the relationship between the numbers in parts c) and d).
Question d) is the side and question c) is the area. When you square the side you get the area. So 3x3=9 .
Here is a video of how to find the square root of a number.
Please comment if you see any mistakes or any ideas to make it better.