8th Maths : Chapter 1 : Numbers : Square Root: Exercise 1.4 : Text Book Back Exercises Questions with Answers, Solution

**Exercise 1.4**

** **

**1. Fill in the blanks:**

(i) The ones
digit in the square of 77 is___________. **[Answer: 9]**

(ii) The
number of non-square numbers between 24^{2} and 25^{2} is ______. **[Answer: 48]**

(iii) The
number of perfect square numbers between 300 and 500 is ______. **[Answer: 5]**

(iv) If a
number has 5 or 6 digits in it, then its square root will have ___________ digits. **[Answer: 3]**

(v) The value
of √180 lies between integers ______ and ______. **[Answer: 13, 14]**

** **

**2. Say True or False:**

(i) When
a square number ends in 6, its square root will have 6 in the unit’s place. **[Answer: True]**

(ii) A square
number will not have odd number of zeros at the end. **[Answer: True]**

(iii) The
number of zeros in the square of 91000 is 9. **[Answer: False]**

(iv) The
square of 75 is 4925. **[Answer: False]**

(v) The square
root of 225 is 15. **[Answer: True]**

**3. Find the square of the following numbers.**

**(i) 17 (ii) 203 (iii) 1098**

**Solution:**

** **

**4. Examine if each of the following is
a perfect square.**

**(i) 725 (ii) 190 (iii) 841 (iv) 1089**

**(i) 725 (ii) 190 (iii) 841 (iv) 1089**

**Solution:**

**(i) 725**

725 = 5 × 5 × 29 = 5^{2} × 29

Here the second prime factor 29 does not have a pair.

Hence 725 is not a perfect square number.

**(ii) 190**

190 = 2 × 5 × 19

Here the factors 2, 5 and 9 does not have pairs.

Hence 190 is not a perfect square number.

**(iii) 841**

841 = 29 × 29

Hence 841 is a perfect square

**(iv) 1089**

1089 = 3 × 3 × 11 × 11

1089 = 3^{2} × 11^{2}

√1089 = 3 × 11 = 33

Hence 1089 is a perfect square

** **

**5. Find the square root by prime factorisation
method.**

**(i) 144 (ii) 256 (iii) 784 (iv) 1156 (v) 4761 (vi) 9025**

**Solution:**

**(i) 144**

144 = 2 × 2 × 2 × 2 × 3 × 3

√l44 = 2 × 2 × 3 = 12

**(ii) 256**

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

√256 = 2 × 2 × 2 × 2 = 16

**(iii) 784**

784 = 2 × 2 × 2 × 2 × 7 × 7

√784 = 2 × 2 × 2 × 2 × 7 × 7 = 28

**(iv) 1156**

1156 = 2 × 2 × 17 × 17

1156 = 2^{2} × 17^{2}

1156 = (2 × 17)^{2}

∴ √1156 = √(2 × l7)^{2} = 2 × 17 = 34

√1156 = 34

** (v) 4761 **

4761 = 3 × 3 × 23 × 23

4761 = 3^{2} × 23^{2}

4761 = (3 × 23)^{2}

√4761 = √(3 × 23)^{2}

√4761 = 3 × 23

√4761 = 69

**(vi) 9025**

9025 = 5 × 5 × 19 × 19

9025 = 5^{2} × 19^{2}

9025 = (5 × 19)^{2}

√925 = = √ (5 × 19)^{2} = 5 × 19 = 95

** **

**6. Find the square root by long division method.**

**(i) 1764 (ii) 6889 (iii) 11025 (iv) 17956 (v) 418609**

**Solution:**

** **

**7. Estimate the value of the following square roots to the nearest whole
number:**

**(i) √440 (ii) √800 (iii) √1020**

**Solution:**

**(i) √440**

We have 20^{2} = 400

21^{2} = 441

∴ √440 ≃ 21

**(ii) √800**

We have 28^{2} = 784

29^{2} = 841

∴ √800 ≃ 28

**(iii) √1020**

We have 31^{2} = 961

32^{2} = 1024

∴ √1020 ≃ 32.

** **

**8. Find the square root of the following decimal numbers and fractions.**

**(i) 2.89 (ii) 67.24 (iii) 2.0164 (iv) 144/225 (v) **

**Solution:**

**(i) 2.89**

√2.89 = 1.7

**(ii) 67.24 **

√67.24 = 8.2

**(iii) 2.0164**

√2.0164 = 1.42

**(iv) 144/225** = √[144/225] = 12/15

**(v) 7 (18/49)** = √[361/49] = √361/√49 = √19^{2}/√7^{2} =19/7

** **

**9. Find the least number that must be subtracted to 6666 so that it becomes
a perfect square. Also, find the square root of the perfect square thus obtained.
**

**Solution:**

Let us work out the process of finding the square root of 6666
by long division method.

The remainder in the last step is 105. Is if 105 be subtracted
from the given number the remainder will be zero and the new number will be a
perfect square.

∴ The required number is 105. The square number is 6666 − 105 =
6561.

∴ √6561 = 81

** **

**10. Find the least number by which 1800 should be multiplied so that it becomes
a perfect square. Also, find the square root of the perfect square thus obtained.**

**Solution:**

We find 1800 = 2 × 2 × 3 × 3 × 5 × 5 × 2

= 2^{2} × 3^{2} × 5^{2} × 2

Here the last factor 2 has no pair. So if we multiply

1800 by 2, then the number becomes a perfect square.

∴ 1800 × 2 = 3600 is the required perfect square number.

∴ 3600 = 1800 × 2

3600 = 2^{2} × 3^{2} × 5^{2} × 2 × 2

3600 = 2^{2} × 3^{2} × 5^{2} × 2^{2}

= (2 × 3 × 5 × 2)^{2}

√3600 = √(2 × 3 × 5 × 2)^{2}

= 2 × 3 × 5 × 2 = 60

∴ √3600 = 60.

** **

**Objective
Type Questions**

**11. The square of 43 ends with the digit ______.**

(A) 9

(B) 6

(C) 4

(D) 3

**[Answer: (A) 9]**

**Solution:** Ones
digit = 3 × 3 = 9

**12. _______ is added to 24 ^{2} to get 25^{2}.**

(A) 4^{2}

(B) 5^{2}

(C) 6^{2}

(D) 7^{2}

**[Answer: (A) 7 ^{2}]**

**Solution:**

25^{2} = 25 × 25 = 625

24^{2} = 24 × 24 = 576

625 −576 = 49

49 = 7^{2}

**13. √48 is approximately equal to ______.**

(A) 5

(B) 6

(C) 7

(D) 8

**[Answer: (C) 7]**

**Solution:
√**49 = 7

**14. √128 - √98 + √18 = ______.**

(A) √2

(B) √8

(C) √48

(D) √32

**[Answer: (D) **√32**]**

**15. The number of digits in the square root of 123454321 is ______.**

(A) 4

(B) 5

(C) 6

(D) 7

**[Answer: (B) **5**]**

**Solution:**

= [*n* + 1] / 2 = 10/2 = 5

** **

**Answer:**

**Exercise 1.4 **

**1. (i) 9 (ii) 48 (iii)
5 (iv) 3 (v) 13, 14 **

**2. (i) True (ii) True (iii)
False (iv) False (v) True **

**3. (i) 289 (ii) 41209 (iii)
1205604 **

**4. (i) No (ii) No (iii)
Yes (iv) Yes**

**5. (i) 12 (ii) 16 (iii)
28 (iv) 34 (v) 69 (vi) 95 **

**6. (i) 42 (ii) 83 (iii)
105 (iv) 134 (v) 647 **

**7. (i) 21 (ii) 28 (iii)
32**

**8. (i) 1.7 (ii) 8.2 (iii)
1.42 (iv) 12/15 (v) 2 5/7 **

**9. 105, 81 10. 2, 60 **

**11. (A) 9 **

**12. (D) 7 ^{2} **

**13. (C) 7 **

**14. (D) √32 **

**15. (B) 5**

** **

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8th Maths : Chapter 1 : Numbers : Exercise 1.4 (Square Root) | Questions with Answers, Solution | Numbers | Chapter 1 | 8th Maths

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