Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 1 Numbers Ex 1.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers Ex 1.4

Question 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 242 and 252 is ________ .
Answer:
48

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

(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 Jii lies between integers ______ and ________ .
Answer:
13, 14

Question 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

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 3.
Find the square of the following numbers.
(i) 17
(ii) 203
(iii) 1098
Answer:
(i) 17
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 1

(ii) 203
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 2

(iii) 1098
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 3

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 4.
Examine if each of the following is a perfect square.
(i) 725
(ii) 190
(iii) 841
(iv) 1089
Answer:
(i) 725
725 = 5 × 5 × 29 = 52 × 29
Here the second prime factor 29 does not have a pair.
Hence 725 is not a perfect square number.
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 4

(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.
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 5

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

(iii) 841
841 = 29 × 29
Hence 841 is a perfect square

(vi) 1089
1089 = 3 × 3 × 11 × 11 = 33 × 33
Hence 1089 is a perfect square

Question 5.
Find the square root by prime factorisation method.
(i) 144
(ii) 256
(iii) 784
(iv) 1156
(v) 4761
(vi) 9025
Answer:
(i) 144
144 = 2 × 2 × 2 × 2 × 3 × 3
√144 = 2 × 2 × 3 = 12
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 6

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

(ii) 256
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
√256 = 2 × 2 × 2 × 2 = 16
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 7

(iii) 784
784 = 2 × 2 × 2 × 2 × 7 × 7
√784 = 2 × 2 × 2 × 2 × 7 × 7 = 28
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 8

(iv) 1156
1156 = 2 × 2 × 17 × 17
1156 = 22 × 172
1156 = (2 × 17)2
∴ \(\sqrt{1156}\) = \(\sqrt{(2 \times 17)^{2}}\) = 2 × 17 = 34
∴ \(\sqrt{1156}\) = 34
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 9

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

(v) 4761
4761 = 3 × 3 × 23 × 23
4761 = 32 × 232
4761 = (3 × 23)2
√4761 = \(\sqrt{(3 \times 23)^{2}}\)
√4761 = 3 × 23
√4761 = 69
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 10

(vi) 9025
9025 = 5 × 5 × 19 × 19
9025 = 52 × 192
9025 = (5 × 19)2
√925 = \(\sqrt{(5 \times 19)^{2}}\) = 5 × 19 = 95
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 11

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 6.
Find the square root by long division method.
(i) 1764
(ii) 6889
(iii) 11025
(iv) 17956
(v) 418609
Answer:
(i) 1764
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 12
√1764 = 42

(ii) 6889
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 13
√6889 = 83

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

(iii) 11025
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 14
√11025 = 105

(iv) 17956
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 15
√17956 = 134

(v) 418609
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 16
√418609 = 647

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 7.
Estimate the value of the following square roots to the nearest whole number:
(i) √440
(ii) √800
(iii) √1020
Answer:
(i) √440
we have 202 = 400
212= 441
∴ √440 ≃ 21

(ii) √800
we have 282 = 784
292= 841
∴ √800 ≃ 28

(iii) √1020
we have 312 = 961
322= 1024
∴ √1020 ≃ 32

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 8.
Find the square root of the following decimal numbers and fractions.
(i) 2.89
(ii) 67.24
(iii) 2.0164
(iv) \(\frac{144}{225}\)
(v) \(7 \frac{18}{49}\)
Answer:
(i) 2.89
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 17
√2.89 = 1.7

(ii) 67.24
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 18
√67.24 = 8.2

(iii) 2.0164
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 19
√2.0164 = 1.42

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

(iv) \(\frac{144}{225}\)
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 20

(v) \(7 \frac{18}{49}\)
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 21
\(\sqrt{7 \frac{18}{49}}=2 \frac{5}{7}\)

Question 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.
Let us work out the process of finding the square root of 6666 by long division method.
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 22
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.

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 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.
Answer:
We find 1800 = 2 × 2 × 3 × 3 × 5 × 5 × 2
= 22 × 32 × 52 × 2
Here the last factor 2 has no pair. So if we multiply 1800 by 2, then the number becomes a perfect square.
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 23
∴ 1800 × 2 = 3600 is the required perfect square number.
∴ 3600 = 1800 × 2
3600 = 22 × 32 × 52 × 2 × 2
3600 = 22 × 32 × 52 × 22
= (2 × 3 × 5 × 2)2
\(\sqrt{3600}=\sqrt{(2 \times 3 \times 5 \times 2)^{2}}\)
= 2 × 3 × 5 × 2 = 60
∴ √3600 = 60

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Objective Type Questions

Question 11.
The square of 43 ends with the digit .
(A) 9
(B) 6
(C) 4
(D) 3
Answer:
(A) 9
Hint:
Ones digit = 3 × 3 = 9

Question 12.
_______ is added to 242 to get 252.
(A) 42
(B) 52
(C) 62
(D) 72
Answer:
(D) 72
Hint:
252 = 25 × 25 = 625
242 = 24 × 24 = 576
Samacheer Kalvi 8th Maths Guide Answers Chapter 1 Numbers Ex 1.4 24

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 13.
√48 is approximately equal to .
(A) 5
(B) 6
(C) 7
(D) 8
Answer:
(C) 7
Hint:
√49 = 7

Question 14.
\(\sqrt{128}-\sqrt{98}+\sqrt{18}\)
(A) √2
(B) √8
(C) √48
(D) √32
Answer:
(D) √32

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Question 15.
The number of digits in the square root of 123454321 is ______.
(A) 4
(B) 5
(C) 6
(D) 7
Answer:
(B) 5
Hint:
\(\frac{n+1}{2}=\frac{10}{2}=5\)

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