Exercise 3A
Question 1
Using the prime factorization method, find which of the following numbers are not perfect squares:
(i) 400
(ii) 768
(iii) 1296
(iv) 8000
(v) 9025
Question 2
Find the smallest number by which each of the given numbers must be multiplied so that the product is a perfect square :
(i) 512
(ii) 700
(iii) 1323
(iv) 35280
Question 3
Find the smallest number by which each of the given numbers should be divided so that the result is a perfect square :
(i) 180
(ii) 1575
(iii) 6912
(iv) 19200
Question 4
Answer True (T) or False (F) :
(i) The number of digits in a square number are always even.
(ii) The square of a prime number is prime.
(iii) No square number is negative.
(iv) The difference of two square numbers is a square number.
(v) 4000 is a square number.
Question 5
Just by looking at the following numbers, give reasons why they are not perfect squares.
(i) 2367
(ii) 57000
(iii) 35943
(iv) 4368
(v) 333222
Question 6
What will be the units digit of the squares of the following numbers ?
(i) 539
(ii) 731
(iii) 8593
(iv) 23904
(v) 39487
(vi) 39065
(vii) 7358
(viii) 5980
Question 7
Fill in the blanks : (Use a property of square numbers)
(i) $19^{2}-18^{2}$=___
(ii) $30^{2}-29^{2}$=___
(iii) $87^{2}-86^{2}$=___
Question 8
Without adding, match the sum in Column A with the perfect square in Column B.
| Column A | Column B |
| (i) 1+3+5+7+9 (ii) 1+3+5+7+9+11+13+15 (iii) 1+3+5 (iv) 1+3+5+7+9+11 (v) 1+3+5+7+9+11+13+15+17+19 | (a) 36 (b) 100 (c) 25 (d) 64 (e) 9 |
Question 9
Which of the following triplets are Pythagorean ?
(i) (10,24,26)
(ii) (14,48,50)
(iii) (18,79,82)
(iv) (22,120,122)
Multiple Choice Questions (MCQs)
Question 10
10. Which number is NOT a perfect square ?
(a) 64
(b) 169
(c) 288
(d) 400
Question 11
The smallest number by which 980 must be multiplied so that the product is a perfect square is
(a) 7
(b) 5
(c) 3
(d) 6
Question 12
For every natural number ' n ', $(n+1)^{2}-n^{2}$ equals.
(a) n-(n+1)
(b) (n+1)-n
(c) (n-1)+n
(d) (n+1)+n
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