Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2

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Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2

Question 1.
Fill in the blanks:
(i) If a number has 5 or 6 digits in it then, its square root will have………digits.
(ii) The value of 180 lies between integers………and……….
(iii) \(\sqrt{10}\) × \(\sqrt{6}\) × \(\sqrt{15}\) =……………
(iv) \(\frac{\sqrt{300}{\sqrt{192}}\) =…………….
(v) \(\sqrt{65.61}\) =…………….
Solution:
(i) 3
(ii) 13, 14
(iii) 30
(iv) \(\frac{5}{4}\)
(v) 8.1

Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Ex 1.2

Question 2.
Estimate the value of the following square roots to the nearest whole number:
(i) \(\sqrt{440}\)
(ii) \(\sqrt{800}\)
(iii) \(\sqrt{1020}\)
Solution:
(i) We have 20² = 400
21² = 441
∴ \(\sqrt{440}\)  \(\widetilde { – } \) 21

(ii) We have 28² = 784
29² = 841
∴ \(\sqrt{800}\) \(\widetilde { – } \) 28

(iii) We have 31² = 961
32² = 1024
∴ \(\sqrt{1020}\) \(\widetilde { – } \) = 32

Question 3.
Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square.
Solution:
We work out the process of finding square root by long division method.
The given number is 1300
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 1
So we have 36² < 1300 < 37²
Also 1300 is (469 – 400) = 69 less than 37². So if we add 69 to 1300 it will be perfect square. Hence the required, least number is 69 and the perfect square number is 1300 + 69 = 1369
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 2
∴ \(\sqrt{1369}\) = 37

Question 4.
Find the least number that must be subtracted to 6412 so as to get a perfect square. Also find the square root of the perfect square.
Solution:
Let us work out the process of finding the square root of 6412 by long division method.
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 3
The remainder in the last step is 12. Is if 12 be subtracted from the given number the remainder will be zero and the new number will be a perfect square.
∴ The required number is 12.
The square number is 6412 – 12 = 6400
Also \(\sqrt{6400}\) = 80

Question 5.
Find the square root by long division method.
(i) 17956
(ii) 11025
(iii) 6889
(iv) 1764
(v) 418609
Solution:
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 4
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 5

Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Ex 1.2

Question 6.
Find the square root of the following decimal numbers:
(i) 2.89
(ii) 1.96
(iii) 67.24
(iv) 31.36
(v) 2.0164
(vi) 13.9876
Solution:
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 6

Question 7.
Find the square root of each of the following fractions:
(i) \(\frac{144}{225}\)
(ii) 7\(\frac{18}{49}\)
(iii) 6\(\frac{1}{4}\)
(iv) 4\(\frac{25}{36}\)
Solution:
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 7
Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Numbers Ex 1.2 8

Question 8.
Say True or False:
(i) \(\frac{\sqrt{32}}{\sqrt{8}}=2\)
(ii) \(\sqrt{\frac{625}{1024}}=\frac{25}{32}\)
(iii) \(\sqrt{28}{7}=2\sqrt{7}\)
(iv) \(\sqrt{225}{64}=\sqrt{289}\)
(v) \(\sqrt{1 \frac{400}{441}}=1 \frac{20}{21}\)
Solution:
(i) true
(ii) true
(iii) false
(iv) false
(v) false

Objective Type Questions

Question 9.
\(\sqrt{48}\) is approximately equal to
(a) 5
(b) 6
(c) 7
(d) 8
Solution:
(c) 7
Hint:
\(\sqrt{49}\) = 7

Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 1 Ex 1.2

Question 10.
\(\sqrt{128}\) – \(\sqrt{98}\) + \(\sqrt{18}\) =
(a) \(\sqrt{2}\)
(b) \(\sqrt{8}\)
(c) \(\sqrt{48}\)
(d) \(\sqrt{32}\)
Solution:
(d) \(\sqrt{32}\)
Hint:
\(\sqrt{128}-\sqrt{98}+\sqrt{18}=8 \sqrt{2}-7 \sqrt{2}+3 \sqrt{2}=4 \sqrt{2}=\sqrt{32}\)

Question 11.
\(\sqrt{22+\sqrt{7+\sqrt{4}}}=\)
(a) \(\sqrt{25}\)
(b) \(\sqrt{33}\)
(c) \(\sqrt{31}\)
(d) \(\sqrt{29}\)
Solution:
(a) \(\sqrt{25}\)
Hint:
\(\sqrt{22+\sqrt{7+\sqrt{4}}}=\sqrt{22+\sqrt{7+2}}=\sqrt{22+3}=\sqrt{25}\)

Question 12.
The number of digits in the square root of 123454321 is
(a) 4
(b) 5
(c) 6
(d) 7
Solution:
(b) 5
Hint:
\(=\frac{n+1}{2}=\frac{10}{2}=5\)