Page 1 - Lesson Notes

SAI International School
Class VIII

Mathematics

Chapter 6-Square and Square roots
Lesson notes
Subtopic: Pythagorean triplet & Square numbers

SUBTOPICS: FINDING SQUARE OF A NUMBER, PYTHAGOREAN TRIPLETS

We can use
2
2
2
 (a+b) = a +b + 2ab

2
2
2
 (a-b) = a +b - 2ab

To find the square of any large number easily.

2
2
Example 1: 45 = (40+5)
2
2
= 40 + 5 + 2*40*5
= 1600+ 25+ 400
= 2025

2
2
Example 2: 67 = (70-3)
2
2
= 70 + 3 - 2*70*3
= 4900+ 9 - 420
= 4489

Consider the following pattern:
2
25 = 625 = (2 × 3) hundreds + 25

2
35 = 1225 = (3 × 4) hundreds + 25

2
75 = 5625 = (7 × 8) hundreds + 25

2
125 = 15625 = (12 × 13) hundreds + 25

Q. Find the square of 45 using above pattern.
2
Ans: 45
(4× 5) hundreds + 25= 2025

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