Square And Square roots Class 8 Important questions worksheet

(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
$\sqrt {18496} =2 \times 2 \times 2 \times 17=136$

(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
$\sqrt {5625} =3 \times 5 \times 5 =75$

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

(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 $5^2=25$

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

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

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

(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
$\sqrt {484} =2 \times 11 =22$

$ \sqrt {176 + \sqrt {2401}} = \sqrt {176 + 49} = \sqrt {225} =15$

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

$\sqrt {83.3569}=9.13$

(i)8
(ii) smaller
(iii) even
(iv) 64
(v) 9
(vi) 39

(i)True
(ii) True
(iii) True
(iv) False
(v) True
(vi) False

13. (b)
14. (a)
15. (a)
16. (c)
17. (d)
$a =\sqrt {234.09} = 15.3$
Perimeter=4a=61.2m
18. (b)
$\sqrt {1 + \frac {25}{144}} = 1 + \frac {x}{12}$
$\sqrt { \frac {169}{144}}= 1 + \frac {x}{12}$
$\frac {13}{12} =1 + \frac {x}{12}$
$x=1$
19 . (c)
if $\sqrt {5625} =75$, then
$\sqrt {0.5625} + \sqrt {56.25}= .75 + 7.5= 8.25$
20. (b)

(p) -> (iv)
(q) -> (i)
(r) -> (iii)
(s) -> (ii)