You are here
Checking if Perfect Cube
Last updated at July 30, 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
Checking if Perfect Cube We follow these steps We do prime factorization of the number If the prime factorization forms triplets, then it is a perfect cube If it doesn’t, then it isn't a perfect cube Let’s take some examples Is 216 a perfect cube? Let’s do prime factorization of 216 Thus, 216 = 2 × 2 × 2 × 3 × 3 × 3 Since 2 & 3 occur in triplets. ∴ 216 is a perfect cube. Is 10648 a perfect cube? Doing Prime factorization of 10648 We see that 10648 = 2 × 2 × 2 × 11 × 11 × 11 Since 2 & 11 occurs in triplets. ∴ 10648 is a perfect cube. Cube root of 10648 = 2 × 11 = 22 Is 5324 a perfect cube? Doing Prime factorization of 5324 We see that 5324 = 2 × 2 × 11 × 11 × 11 Since 2 does not occur in triplets. ∴ 5324 is not a perfect cube. Is 400 a perfect cube? Doing Prime factorization of 400 We see that 400 = 2 × 2 × 2 × 2 × 5 × 5 Since 2 & 5 do not occur in triplets. ∴ 400 is not a perfect cube.
