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Mathematics
Squares And Square Roots
NCERT Solutions
NCERT Solutions
Squares And Square Roots
30 Solutions
Exercise:
All Exercises
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
Q1
Exercise 5.1
What will be the unit digit of the squares of the following numbers?
(i)
81
(ii)
272
(iii)
799
(iv)
3853
(v)
1234
(vi)
26387
(vii)
52698
(viii)
99880
(ix)
12796
(x)
55555
Q2
Exercise 5.1
The following numbers are obviously not perfect squares. Give reason.
(i)
1057
(ii)
23453
(iii)
7928
(iv)
222222
(v)
64000
(vi)
89722
(vii)
222000
(viii)
505050
Q3
Exercise 5.1
The squares of which of the following would be odd numbers?
(i)
431
(ii)
2826
(iii)
7779
(iv)
82004
Q4
Exercise 5.1
Observe the following pattern and find the missing digits.
11
2
=
121
11^2 = 121
1
1
2
=
121
101
2
=
10201
101^2 = 10201
10
1
2
=
10201
1001
2
=
1002001
1001^2 = 1002001
100
1
2
=
1002001
100001
2
=
1........2........1
100001^2 = 1........2........1
10000
1
2
=
1........2........1
10000001
2
=
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
10000001^2 = ....................
1000000
1
2
=
....................
Q5
Exercise 5.1
Observe the following pattern and supply the missing numbers.
11
2
=
121
11^2 = 121
1
1
2
=
121
101
2
=
10201
101^2 = 10201
10
1
2
=
10201
10101
2
=
102030201
10101^2 = 102030201
1010
1
2
=
102030201
1010101
2
=
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1010101^2 = ....................
101010
1
2
=
....................
.
.
.
.
.
.
.
.
.
.
.
2
=
10203040504030201
...........^2 = 10203040504030201
..........
.
2
=
10203040504030201
Q6
Exercise 5.1
Using the given pattern, find the missing numbers.
1
2
+
2
2
+
2
2
=
3
2
1^2+2^2+2^2=3^2
1
2
+
2
2
+
2
2
=
3
2
2
2
+
3
2
+
6
2
=
7
2
2^2+3^2+6^2=7^2
2
2
+
3
2
+
6
2
=
7
2
3
2
+
4
2
+
12
2
=
13
2
3^2+4^2+12^2=13^2
3
2
+
4
2
+
1
2
2
=
1
3
2
4
2
+
5
2
+
.
.
.
2
=
21
2
4^2+5^2+...^2=21^2
4
2
+
5
2
+
..
.
2
=
2
1
2
5
2
+
.
.
.
+
30
2
=
31
2
5^2+...+30^2=31^2
5
2
+
...
+
3
0
2
=
3
1
2
6
2
+
7
2
+
.
.
.
2
=
.
.
.
2
6^2+7^2+...^2=...^2
6
2
+
7
2
+
..
.
2
=
..
.
2
Q7
Exercise 5.1
Without adding, find the sum.
(i)
1
+
3
+
5
+
7
+
9
1+3+5+7+9
1
+
3
+
5
+
7
+
9
(ii)
1
+
3
+
5
+
7
+
9
+
11
+
13
+
15
+
17
+
19
1+3+5+7+9+11+13+15+17+19
1
+
3
+
5
+
7
+
9
+
11
+
13
+
15
+
17
+
19
(iii)
1
+
3
+
5
+
7
+
9
+
11
+
13
+
15
+
17
+
19
+
21
+
23
1+3+5+7+9+11+13+15+17+19+21+23
1
+
3
+
5
+
7
+
9
+
11
+
13
+
15
+
17
+
19
+
21
+
23
Q8
Exercise 5.1
(i)
Express 49 as the sum of 7 odd numbers.
(ii)
Express 121 as the sum of 11 odd numbers.
Q9
Exercise 5.1
How many numbers lie between squares of the following numbers?
(i)
12 and 13
(ii)
25 and 26
(iii)
99 and 100
Q1
Exercise 5.2
Find the square of the following numbers.
(i)
32
(ii)
35
(iii)
86
(iv)
93
(v)
71
(vi)
46
Q2
Exercise 5.2
Write a Pythagorean triplet whose one member is.
(i)
6
(ii)
14
(iii)
16
(iv)
18
Q1
Exercise 5.3
What could be the possible 'one's' digits of the square root of each of the following numbers?
(i)
9801
(ii)
99856
(iii)
998001
(iv)
657666025
Q2
Exercise 5.3
Without doing any calculation, find the numbers which are surely not perfect squares.
(i)
153
(ii)
257
(iii)
408
(iv)
441
Q3
Exercise 5.3
Find the square roots of 100 and 169 by the method of repeated subtraction.
Q4
Exercise 5.3
Find the square roots of the following numbers by the Prime Factorisation Method.
(i)
729
(ii)
400
(iii)
1764
(iv)
4096
(v)
7744
(vi)
9604
(vii)
5929
(viii)
9216
(ix)
529
(x)
8100
Q5
Exercise 5.3
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i)
252
(ii)
180
(iii)
1008
(iv)
2028
(v)
1458
(vi)
768
Q6
Exercise 5.3
For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.
(i)
252
(ii)
2925
(iii)
396
(iv)
2645
(v)
2800
(vi)
1620
Q7
Exercise 5.3
The students of Class VIII of a school donated ₹ 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Q8
Exercise 5.3
2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Q9
Exercise 5.3
Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
Q10
Exercise 5.3
Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Q1
Exercise 5.4
Find the square root of each of the following numbers by Division method.
(i)
2304
(ii)
4489
(iii)
3481
(iv)
529
(v)
3249
(vi)
1369
(vii)
5776
(viii)
7921
(ix)
576
(x)
1024 (xi) 3136 (xii) 900
Q2
Exercise 5.4
Find the number of digits in the square root of each of the following numbers (without any calculation).
(i)
64
(ii)
144
(iii)
4489
(iv)
27225
(v)
390625
Q3
Exercise 5.4
Find the square root of the following decimal numbers.
(i)
2.56
(ii)
7.29
(iii)
51.84
(iv)
42.25
(v)
31.36
Q4
Exercise 5.4
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i)
402
(ii)
1989
(iii)
3250
(iv)
825
(v)
4000
Q5
Exercise 5.4
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i)
525
(ii)
1750
(iii)
252
(iv)
1825
(v)
6412
Q6
Exercise 5.4
Find the length of the side of a square whose area is
441
m
2
441 \text{ m}^2
441
m
2
.
Q7
Exercise 5.4
In a right triangle ABC,
∠
B
=
90
∘
\angle B = 90^\circ
∠
B
=
9
0
∘
.
(a)
If AB = 6 cm, BC = 8 cm, find AC
(b)
If AC = 13 cm, BC = 5 cm, find AB
Q8
Exercise 5.4
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
Q9
Exercise 5.4
There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.
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