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Perfect Squares and Triangular Numbers
Last updated at July 29, 2025 by Teachoo
Class 8 (Ganita Prakash & Old NCERT)
Chapter 1 Class 8 - A Square and a Cube (Ganita Prakash)
- Introduction
- Square Numbers
- Perfect Squares - and its Properties
-
Perfect Squares - and its Patterns
- Square Root
- Smallest number multiply or divide to get perfect square
- Estimating Square Root
- Figure it out - Page 10, 11
- Cubic Numbers
- Perfect Cubes - and its Properties
- Perfect Cubes - and its Patterns
- Cube Root
- Smallest number multiply or divide to get perfect cube
- A pinch of History
- Figure it out - Page 16, 17
Transcript
Perfect Squares and Triangular Numbers Triangular numbers is the sequence 1, 3, 6, 10, 15, … What if we add consecutive triangular numbers? Example: Let’s add 3 + 6 = 9 Similarly, we can see Adding pairs of consecutive triangular numbers: 1 + 3 = 4 3 + 6 = 9 6 + 10 = 16 10 + 15 = 25 15 + 21 = 36 This gives the Square Numbers sequence: 4, 9, 16, 25, 36, ... → which are 2², 3², 4², 5², 6², ... We can also try visualizing it Rotate the 3 dots and adjust it over the 6 dots If you rotate all 9 dots, it becomes a perfect square
