RS Aggarwal Solutions: Exercise 3H - Squares and Square Roots | Mathematics (Maths) Class 8 PDF Download

Q.1. Which of the following numbers is not a perfect square?
(a) 7056
(b) 3969
(c) 5478
(d) 4624
Ans. (c) 5478
According to the properties of squares, a number ending in 2, 3, 7 or 8 is not a perfect square.

Q.2. Which of the following numbers is not a perfect square?
(a) 1444
(b) 3136
(c) 961
(d) 2222
Ans. (d) 2222
According to the property of squares, a number ending in 2, 3, 7 or 8 is not a perfect square.

Q.3. Which of the following numbers is not a perfect square?
(a) 1843
(b) 3721
(c) 1024
(d) 1296
Ans. (a) 1843
According to the property of squares, a number ending in 2, 3, 7 and 8 is not a perfect square.

Q.4. Which of the following numbers is not a perfect square?
(a) 1156
(b) 4787
(c) 2704
(d) 3969
Ans. (b) 4787
By the property of squares, a number ending in 2, 3,7 or 8 is not a perfect square.

Q.5. Which of the following numbers is not a perfect square?
(a) 3600
(b) 6400
(c) 81000
(d) 2500
Ans. (c) 81000
According to the property of squares, a number ending in odd number of zeroes is not a perfect square.

Q.6. Which of the following cannot be the unit digit of a perfect square number?
(a) 6
(b) 1
(c) 9
(d) 8
Ans. (d) 8
According to the property of squares, a perfect square cannot have 2, 3, 7 or 8 as the unit digit.

Q.7. The square of a proper fraction is
(a) larger than the fraction
(b) smaller than the fraction
(c) equal to the fraction
(d) none of these
Ans. (b) smaller than the fraction

Q.8. If n is odd, then (1 + 3 + 5 + 7 +... to n terms) is equal to
(a) (n² + 1)
(b) (n² − 1)
(c) n²
(d) (2n² + 1)
Ans. (c) n²

Q.9. Which of the following is a pythagorean triplet?
(a) (2, 3, 5)
(b) (5, 7, 9)
(c) (6, 9, 11)
(d) (8, 15, 17)
Ans. (d) (8,15,17)
This can be understood from the property of Pythagorean triplets. According to this property, for a natural number m, (2m, m²−1, m²+1) is a Pythagorean triplet.
Here,  m = 4
2m = 8
m² - 1=15
and m² + 1 = 17

Q.10. What least number must be subtracted from 176 to make it a perfect square
(a) 16
(b) 10
(c) 7
(d) 4
Ans. (c) 7
(176−7)=169
√169=13

Q.11. What least number must be added to 526 to make it a perfect square?
(a) 3
(b) 2
(c) 1
(d) 6
Ans. (a) 3
526+3=529
529=23²

Q.12. What least number must be added to 15370 to make it a perfect square?
(a) 4
(b) 6
(c) 8
(d) 9
Ans. (b) 6
15370+6=15376
=124

Q.13.= ?
(a) 0.3
(b) 0.03
(c) 0.33
(d) 0.94
Ans. (d) 0.94

√0.9=0.94

Q.14.=?
(a) 0.1
(b) 0.01
(c) 0.316
(d) none of these
Ans. (c) 0.316
Using long division method:

∴ √0.1= 0.316

Q.15.
(a) 0.12
(b) 1.2
(c) 0.75
(d) 12
Ans. (b) 1.2
= 1.2

Q.16.
(a) √3/2
(b) 3/√2
(c) 3/2
(d) 1.49
Ans. (c) 3/2
= 3/2

Q.17.

(d) none of these
Ans. (b)


Q.18. Which of the following is the square of an even number?
(a) 196
(b) 441
(c) 625
(d) 529
Ans. (a) 196
Square of an even number is always an even number.

Q.19. Which of the following is the square of an odd number?
(a) 2116
(b) 3844
(c) 1369
(d) 2500
Ans. (c) 1369
Square of an odd number is always an odd number.