Page 45 - ICSE Math 8

EXERCISE 3.2

1. Which of the following numbers are not perfect squares? Give reasons.

(a) 7,921 (b) 4,205 (c) 2,209 (d) 7,442
2. Which of the following numbers will have their squares as odd numbers?
(a) 131 (b) 2,136 (c) 4,259 (d) 628 (e) 104
3. What will be the units digit of the squares of the following numbers?
(a) 62 (b) 6,555 (c) 277 (d) 7,431 (e) 1,832
4. Observe the following pattern and write the value of 1 + 3 + 5 + 7 + 9 + 11 + ... + 27.
1 + 3 = 4 = 2 2

1 + 3 + 5 = 9 = 3 2
1 + 3 + 5 + 7 = 16 = 4 2
1 + 3 + 5 + 7 + 9 = 25 = 5 2
2
5. Observe the following pattern and find the value of 10101010101 .
2
11 = 121
2
101 = 10201
2
10101 = 102030201
2
1010101 = 1020304030201
2
2
2
6. Observe the following pattern and find the value of: (a) 45 – 44 (b) 132 – 131 2
2
2
2 – 1 = 2 + 1
2
2
3 – 2 = 3 + 2
2
2
4 – 3 = 4 + 3
2
2
5 – 4 = 5 + 4
7. Write a Pythagorean triplet whose members are formed by the given natural numbers.
(a) 6 (b) 14 (c) 16 (d) 8
8. Which of the following numbers are squares of even numbers?
(a) 1,225 (b) 256 (c) 2,704 (d) 841 (e) 2,304
Square Roots
Square root of a number n is that number which when multiplied by Try This
itself gives n as the product. In other words, if n is the given number and Find the square roots of:
2
m is its square root, then n = m . Square root is represented by the symbol (i) 81 (ii) 400 (iii) 049
‘ ’ , i.e., n = . m

For example, 4 = 2 16 ⇒ 16 = 4 ; 5 = 2 25 ⇒ 25 = 5 ; 13 = 2 169 ⇒ 169 13= , and so on.

Properties of square roots
Let’s continue with what you have learnt about the properties of squares and apply them to the properties of
square roots.
1. A number ending with 2, 3, 7 or 8 does not have a natural number as its square root.
2. A number ending with odd number of zeros does not have a natural number as its square root.
However, if a number ends with even number of zeros, its square root is a natural number ending with
half the number of zeros than the given number.

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