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Estimating Square Root
Last updated at July 30, 2025 by Teachoo
Estimating Square Root
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
Estimating Square Root For larger numbers, we can estimate (guess) the square root. Letβs taken example Find βππππ using estimation We know 402 = 1600 and 502 = 2500. So, the root is between 40 and 50. The number 1936 ends in 6, so its square root must end in 4 or 6. The possibilities are 44 or 46. Let's check the midpoint: 452 =2025. Since 1936 is less than 2025, the root must be less than 45. The only possibility is 44. Let's verify: 442 = 1936. Correct Find βπππ using estimation We know 102 = 100 and 202 = 400. So, the root is between 10 and 20. The number 250 ends in 0, since it is a single 0 (odd number of zero), we know it is not a perfect square Let's check the midpoint: 152 = 225 So, letβs do 162 also, 162 = 256 Thus, 15 < βπππ < 16. Since 256 is much closer to 250 than 225, βπππ is approximately 16. This type of estimation will help when we have to find approximate square root
