Page 4 - NCERT Books

92 MATHEMATICS

We can see that when a square number ends in 6, the number whose square it is, will
have either 4 or 6 in unit’s place.
Can you find more such rules by observing the numbers and their squares (Table 1)?

TRY THESE

What will be the “one’s digit” in the square of the following numbers?
(i) 1234 (ii) 26387 (iii) 52698 (iv) 99880
(v) 21222 (vi) 9106

• Consider the following numbers and their squares.
2
10 = 100
We have 20 = 400 But we have
2
one zero two zeros
2
80 = 6400
100 = 10000
2
2
200 = 40000
We have But we have
2
two zeros 700 = 490000 four zeros
2
900 = 810000
If a number contains 3 zeros at the end, how many zeros will its square have ?
What do you notice about the number of zeros at the end of the number and the
number of zeros at the end of its square?
Can we say that square numbers can only have even number of zeros at the end?
• See Table 1 with numbers and their squares.
What can you say about the squares of even numbers and squares of odd numbers?

TRY THESE

1. The square of which of the following numbers would be an odd number/an even
number? Why?
(i) 727 (ii) 158 (iii) 269 (iv) 1980
2. What will be the number of zeros in the square of the following numbers?
(i) 60 (ii) 400

6.3 Some More Interesting Patterns
1. Adding triangular numbers.
Do you remember triangular numbers (numbers whose dot patterns can be arranged
as triangles)?
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1 3 6 10 15