Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

Samacheer Kalvi 8th Maths Guide Chapter 1 Numbers Ex 1.4

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

 

(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

 

Question 3.
Find the square of the following numbers.
(i) 17
(ii) 203
(iii) 1098
Answer:
(i) 17

(ii) 203

(iii) 1098

 

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.

(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

(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

 

(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

(vi) 9025
9025 = 5 × 5 × 19 × 19
9025 = 5² × 19²
9025 = (5 × 19)²

(ii) 6889

√6889 = 83

 

(iii) 11025

√11025 = 105

(iv) 17956

√17956 = 134

(v) 418609

√418609 = 647

 

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

(iii) 2.0164

√2.0164 = 1.42

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.

 

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.

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

 

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

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