Exercise 1.4 - Chapter 1 Numbers 8th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

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

(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:

Question $4 .$
Examine if each of the following is a perfect square.
(i) 725
(ii) 190
(iii) 841
(iv) 1089
Answer:
(i) 725
$725=5 \times 5 \times 29=5^{2} \times 29$
Here the second prime factor 29 does not have a pair. Hence 725 is not a perfect square number.

(ii) 190
$190=2 \times 5 \times 19$
Here the factors 2,5 and 9 does not have pairs. Hence 190 is not a perfect square number.

(iii) 841
$841=29 \times 29$
Hence 841 is a perfect square
(vi) 1089
$1089=3 \times 3 \times 11 \times 11=33 \times 33$
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
$144=2 \times 2 \times 2 \times 2 \times 3 \times 3$
$\sqrt{1} 44=2 \times 2 \times 3=12$

(ii) 256
$256=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\sqrt{256}=2 \times 2 \times 2 \times 2=16$

(iii) 784
$784=2 \times 2 \times 2 \times 2 \times 7 \times 7$
$\sqrt{784}=2 \times 2 \times 2 \times 2 \times 7 \times 7=28$

(iv) 1156
$1156=2 \times 2 \times 17 \times 17$
$1156=2^{2} \times 17^{2}$
$1156=(2 \times 17)^{2}$
$\therefore \sqrt{1156}=\sqrt{(2 \times 17)^{2}}=2 \times 17=34$
$\therefore \sqrt{1156}=34$

(v) 4761
$4761=3 \times 3 \times 23 \times 23$
$4761=3^{2} \times 23^{2}$
$4761=(3 \times 23)^{2}$
$\sqrt{4761}=\sqrt{(3 \times 23)^{2}}$
$\sqrt{4761}=3 \times 23$
$\sqrt{4761}=69$

(vi) 9025
$9025=5 \times 5 \times 19 \times 19$
$9025=5^{2} \times 19^{2}$
$9025=(5 \times 19)^{2}$
$\sqrt{925}=\sqrt{(5 \times 19)^{2}}=5 \times 19=95$

Question $6 .$
Find the square root by long division method.
(i) 1764
(ii) 6889
(iii) 11025
(iv) 17956
(v) 418609
Answer:
(i) 1764

Question 7.
Estimate the value of the following square roots to the nearest whole number:
(i) $\sqrt{440}$
(ii) $\sqrt{800}$
(iii) $\sqrt{1020}$
Answer:
(i) $\sqrt{440}$
we have $20^{2}=400$
$21^{2}=441$
$\therefore \sqrt{440} \simeq 21$
(ii) $\sqrt{800}$
we have $28^{2}=784$
$\begin{aligned}
&29^{2}=841 \\
&\therefore \sqrt{800} \simeq 28
\end{aligned}$
(iii) $\sqrt{1020}$
we have $31^{2}=961$
$\begin{aligned}
&32^{2}=1024 \\
&\therefore \sqrt{10} 02 \simeq 32
\end{aligned}$

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:

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.

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.
$\therefore$ 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 $1800=2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 2$ $=2^{2} \times 3^{2} \times 5^{2} \times 2$
Here the last factor 2 has no pair. So if we multiply 1800 by 2 , then the number becomes a perfect square.

$\therefore 1800 \times 2=3600$ is the required perfect square number.
$\begin{aligned}
&\therefore 3600=1800 \times 2 \\
&3600=2^{2} \times 3^{2} \times 5^{2} \times 2 \times 2 \\
&3600=2^{2} \times 3^{2} \times 5^{2} \times 2^{2} \\
&=(2 \times 3 \times 5 \times 2)^{2} \\
&\sqrt{3600}=\sqrt{(2 \times 3 \times 5 \times 2)^{2}} \\
&=2 \times 3 \times 5 \times 2=60 \\
&\therefore \sqrt{3600}=60
\end{aligned}$

Objective Type Questions
Question $11 .$
The square of 43 ends with the digit
(A) 9
(B) 6
(C) 4
(D) 3
Answer:
(A) 9

Question 12 .
__is added to $24^{2}$ to get $25^{2}$.
(A) $4^{2}$
(B) $5^{2}$
(C) $6^{2}$
(D) $7^{2}$
Answer:
(D) $7^{2}$
 

Question $13 .$
$\sqrt{48}$ is approximately equal to .
(A) 5
(B) 6
(C) 7

(D) 8
Answer:
(C) 7
Hint:
$\sqrt{49}=7$
 

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

Question $15 .$
The number of digits in the square root of 123454321 is
(A) 4
(B) 5
(C) 6
(D) 7
Answer:
(B) 5