NCERT Class 8 Maths Chapter 1 A Square and A Cube Solutions
NCERT Class 8 Maths Chapter 1 A Square and A Cube Solutions Patterns and Properties of Perfect Squares (Page 4) Q. 1 Find the squares of the first 30 natural numbers and fill in the table below. Answer: Q 2. What patterns do you notice? Share your observations and make conjectures. Answer: When we look at the squares of the first 30 natural numbers, we notice some patterns: 1. Unit digits pattern The squares always end with 0, 1, 4, 5, 6, or 9. They never end with 2, 3, 7, or 8. 2. Even/Odd relation The square of an even number is always even . The square of an odd number is always odd . 3. Zeros at the end If a number has a zero at the end, its square will have two zeros at the end. In general, squares always have an even number of zeros at the end. 4. Increasing difference The difference between two consecutive squares is always an odd number (e.g., 4 – 1 = 3, 9 – 4 = 5, 16 – 9 = 7, …). Conjecture (what we can guess from the pattern) If a number ends with 2, 3, 7, or 8, it cann...