Square And Square roots Class 8 Important questions worksheet
In this page we have square and square roots class 8 worksheet. This worksheet contains all the format of questions like Multiple choice question,Long answer type questions, Fill in the blanks ,True and False. Hope you like them and do not forget to like , social share
and comment at the end of the page.
Long answer type questions
Question 1
Find the square root of each of the following numbers by using the method of prime factorization:
(a) 121
(b) 441
(c) 625
(d) 729
(e) 1521
(f) 2025
(g) 4096
(h) 5776
(i) 8100
(j) 9216
(k) 11236
(l) 15876
(m) 18496 Solution
(a) 121 = 11 x 11
$\sqrt {121} =11$
(b) 441= 3 x 3 x 7 x 7
$\sqrt {441} =3 \times 7=21$
(c) 625= 5 x 5 x 5 x 5
$\sqrt {625} =5 \times 5=25$
(d) 729= 3 x 3 x 3 x 3 x 3 x 3
$\sqrt {729} =3 \times 3 \times 3=27$
(e)1521= 3 x 3 x 13 x 13
$\sqrt {1521} =3 \times 13=39$
(f) 2025= 3 x 3 x 3 x 3 x 5 x 5
$\sqrt {2025} =3 \times 3 \times 5=45$
(g) 4096=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
$\sqrt {4096} =2 \times 2 \times 2 \times 2 \times 2 \times 2=64$
(h) 5776= 2 x 2 x 2 x 2 x 19 x 19
$\sqrt {5776} =2 \times 2 \times 19=76$
(i) 8100= 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5
$\sqrt {8100} =2 \times 3 \times 3 \times 5=90$
(j) 9216= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3
$\sqrt {9216} =2 \times 2 \times 2 \times 2 \times 2 \times 3=96$
(k)11236 =2 x 2 x 53 x 53
$\sqrt {11236} =2 \times 53=106$
(l) 15876= 2 x 2 x 3 x 3 x 3 x 3 x 7 x 7
$\sqrt {15876} =2 \times 3 \times 3 \times 7=126$
(m) 18496=2 x 2 x 2 x 2 x 2 x 2 x 17 x 17
$\sqrt {18496} =2 \times 2 \times 2 \times 17=136$
Question 2
Find the smallest number by which following number must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.
(i)1008= 2 x 2 x 2 x 2 x 3 x 3 x 7
We can see number 7 is not in pair, So to make a perfect square, it has to be multiplied by 7
Then number will become=7056
Now
7056= 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7
$\sqrt {7056} =2 \times 2 \times 3 \times 7=84$
(ii)1280=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5
We can see number 5 is not in pair, So to make a perfect square, it has to be multiplied by 5
Then number will become=6400
Now
6400= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5
$\sqrt {6400} =2 \times 2 \times 2 \times 2 \times 5=80$
(iii)1875= 3 x 5 x 5 x 5 x 5
We can see number 3 is not in pair, So to make a perfect square, it has to be multiplied by 3
Then number will become=5625
Now
5625= 3 x 3 x 5 x 5 x 5 x 5
$\sqrt {5625} =3 \times 5 \times 5 =75$
Question 3.
676 students are to be sit in a hall in such a way that each row contains as many students as the number of rows. Find the number of rows and the number of students in each row. Solution
Here we need to find the square root of the Number 676
676=2 x 2 x 13 x 13
$\sqrt {676} =2 \times 13 =26$
So There are 26 rows and each rows has 26 students
Question 4.
What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 1801
(ii) 856
(iii) 1008001
(iv) 6577525 Solution
(i)Last digit is 1 , So one digit can be 1 or 9 as $1^2=1$ and $9^2=81$
(ii)Last digit is 5 , So one digit can be 4 or 6 as $4^2=16$ and $6^2=36$
(i)Last digit is 1 , So one digit can be 1 or 9 as $1^2=1$ and $9^2=81$
(i)Last digit is 5 , So one digit will be 5 as $5^2=25$
Question 5.
The students of a class arranged a gift for the class teacher. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 1521, find the strength of the class. Solution
Here we need to find the square root of the Number 1521
1521= 3 x 3 x 13 x 13
$\sqrt {1521} =3 \times 13=39$
So There are 39 students and each contributed has Rs 39
Question 6.
Find the least number which when added to 4529 to make it a perfect square? Solution
Let us find the square root of 4529 using Long division method
So remainder is 40
Therfore $67^2 < 4529$
Next perfect square would be $68^2=4624$
hence the number to be added = 4624 - 4529 = 95
So addition of 95 to 4529 will make it perfect square
Question 7.
Find the least number which must be subtracted from 2361 to make it a perfect square? Solution
Let us find the square root of 2361 using Long division method
So remainder is 57
Therfore $48^2 < 2361$
Now if we subtract the remainder from main number, it will be perfect square
So subtraction of 57 from 2361 will make it perfect square
Question 8
Find the smallest number by which following number must be divided to get a perfect square. Also, find the square root of the perfect square so obtained.
(i)600
(ii)2904 Solution
(i) 600= 2 x 2 x 2 x 3 x 5 x 5
We can see number 2 and 3 is not in pair, So to make a perfect square, it has to be divided by 6
Then number will become=100
Now
100= 2 x 2 x 5 x 5
$\sqrt {100} =2 \times 5 =10$
(ii)2904=2 x 2 x 2 x 3 x 11 x 11
We can see number 2 and 3 is not in pair, So to make a perfect square, it has to be divided by 6
Then number will become=484
Now
484= 2 x 2 x 11 x 11
$\sqrt {484} =2 \times 11 =22$
Question 9
Find the value of
$ \sqrt {176 + \sqrt {2401}}$ Solution
Question 10
Find the square root
(i).0151129
(ii) 83.3569 Solution
Square roots for decimal are found using the same long division method. We put bars on both integral part and decimal part.For integral we move fron the unit's place close to the decimal and move towards left. For decimal part, we start from the decimal and move towards right
(i) By long division method
$\sqrt {.0151129}=.123$
(ii) By long division method
$\sqrt {83.3569}=9.13$
Fill in the blanks
Question 11
(i)There are _________ perfect squares between 1 and 100
(ii) The square of a proper fraction is ______ than to the fraction
(iii) The square of a even number is _____
(iv) $\sqrt{4096}$ is ____
(v) The digit at the ones place of $37^2$ is ____
(vi) the least number that must be added to 1500 so as to get a perfect square is ___ Solution
(i)8
(ii) smaller
(iii) even
(iv) 64
(v) 9
(vi) 39
True and False
Question 12
(i)The square root of 0.64 is 0.8.
(ii) There is no square number between 70 and 80.
(iii)6292 is not a perfect square
(iv) 1000 is a perfect square.
(v) The product of two perfect squares is a perfect square
(vi)The number of digits in a perfect square is even Solution
Question 13
Which of the following is not a perfect square number?
(a) 1156
(b) 4657
(c)4624
(d) 7056 Question 14
A perfect square can never have the following digit in its ones place
(a) 8
(b) 4
(b) 0
(d) 1 Question 15
The sum of first n odd natural numbers is
(a)$n^2$
(b) $2n$
(c) $n^2 +1$
(d) $n^2 -1$ Question 16
$\sqrt {.9} $ is
(a).3
(b) .03
(c).94
(d).33 Question 17
The area of the square field is 234.09 m2. The perimeter of the field id
(a)65.2 m
(b)59.6 m
(c)51.2 m
(d)61.2 m Question 18
The value of x in $\sqrt {1 + \frac {25}{144}} = 1 + \frac {x}{12}$ is
(a)2
(b) 1
(c) 4
(d) 5 Question 19
Given that $\sqrt {5625} =75$, the value of $\sqrt {0.5625} + \sqrt {56.25}$ is:
(a) 82.5
(b) 0.75
(c) 8.25
(d) 75.05 Question 20
Which of the following is a pythogorean triplet?
(a) 2,3,4
(b) 6,8,10
(c) 5,7,9
(d) none of these Solution
This square and square roots class 8 worksheet is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail. You can download this also using the below link
