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CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 7 - MCQExams.com
CBSE
Class 8 Maths
Squares And Square Roots
Quiz 7
Find the value of
√
25
.
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0%
5
0%
−
√
5
0%
√
3
0%
None of these
Explanation
√
25
=
√
5
×
5
=
5
State whether the statements are true (T) or false (F).
If
a
2
ends in 9, then
a
3
ends in 7.
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0%
True
0%
False
Explanation
∵
(
7
)
2
=
49
ends in 9 and
(
7
)
3
=
343
does not ends in 7.
Estimate:
√
60
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0%
7.7
0%
7
0%
7.2
0%
7.5
Explanation
60
is in between two perfect squares:
49
, which is
7
2
and
64
which is
8
2
. The difference between
64
and
49
is
15
so
60
is little more than
2
3
of the way toward
64
from
49
. A reasonable estimate for
√
60
, then would be about
7.7
which is a little more than
2
3
toward
8
from
7
.
127
is a
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0%
irrational number
0%
perfect square
number
0%
non-perfect square
number
0%
real number
Explanation
We know that the number ends with
00
,
1
,
4
,
5
,
6
or
9
are perfect square and natural number is also a real number.
So, 127 is a non-perfect square and a real number.
Identify which one of the following numbers are Pythagorean triplets?
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0%
12
,
35
,
37
0%
15
,
102
,
106
0%
10
,
23
,
26
0%
14
,
28
,
50
Explanation
Taking the case of
12
,
35
,
37
On squaring each number, we get
12
2
=
144
35
2
=
1225
37
2
=
1369
Now,
12
2
+
35
2
=
144
+
1225
=
1369
=
37
2
∴
12
2
+
35
2
=
37
2
Hence,
12
,
35
,
37
are Pythagorean triplets.
10
,
24
and __ will form a Pythagorean triplets.
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0%
25
0%
26
0%
27
0%
28
Explanation
We know that Pythagorean triplets will satisfy the condition,
a
2
+
b
2
=
c
2
c
2
=
10
2
+
24
2
=
100
+
576
=
676
⇒
c
=
26
Thus
10
,
24
and
26
form a Pythagorean triplet
What is the Pythagorean triplets whose one member is
20
?
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0%
20
,
97
,
99
0%
20
,
99
,
101
0%
20
,
197
,
199
0%
20
,
199
,
201
Explanation
For any natural numbers
m
>
1
,
2
m
,
m
2
−
1
,
m
2
+
1
forms a Pythagorean triplet.
If we take
m
2
+
1
=
20
, then
m
2
=
19
The value of m will not be an integer.
If we take
m
2
−
1
=
20
, then
m
2
=
21
Again the value of m will not be an integer.
Let
2
m
=
20
=>
m
=
10
∴
2
m
=
2
⋅
10
=
20
m
2
−
1
=
10
2
−
1
=
99
and
m
2
+
1
=
10
2
+
1
=
101
Therefore, the Pythagorean triplets are
20
,
99
,
101.
What least number must be added to
4812
to make the sum a perfect square? (Use Long division method).
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0%
86
0%
88
0%
89
0%
85
Explanation
The following steps are used to find the square root by long division method:
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
↓
Quotient
↓
69
6
¯
48
¯
12
36
_
_
129
1212
1161
_
51
Here, the remainder
=
51
We observe here
69
2
<
4812
<
70
2
The required number to be added
=
70
2
−
4812
=
4900
−
4812
=
88
Therefore,
88
must be added to
4812
to make it a perfect square.
Find the square root of
12.25
using long division method.
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0%
3.2
0%
3.4
0%
3.5
0%
3.1
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
↓
Quotient
↓
3.5
3
¯
12
.
¯
25
9
______
6.5
3.25
3.25
______
0
←
Remainder
√
12.25
=
3.5
What least number must be added to 700 to make the sum a perfect square? (Use Long division method).
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0%
25
0%
26
0%
28
0%
29
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
↓
Quotient
↓
26
2
¯
7
¯
00
4
46
300
276
24
←
Remainder
We observe here
26
2
<
700
<
27
2
The required number to be added =
27
2
−
700
= 729 - 700
= 29
Therefore, 29 must be added to 700 to make it a perfect square.
State whether the statements are true (T) or false (F).
All numbers of a Pythagorean triplet are odd.
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0%
True
0%
False
Explanation
For Pythagorean triplet square of one should be equal to sum of square of other two.
Means, Pythagorean triplet as
5
2
=
4
2
+
3
2
Here, 4 is an even number.
State whether the statements are true (T) or false (F).
The square root of 0.9 is 0.3.
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0%
True
0%
False
Explanation
The square of 0.3 =
(
0.3
)
2
=
0.3
×
0.3
=
0.09
Which least number must be subtracted to
1025
to make a perfect square? (Use Long division method).
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0%
1
0%
2
0%
3
0%
4
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
↓
Quotient
↓
32
3
¯
10
¯
25
9
62
125
124
1
←
Remainder
The remainder is 1. it represents that the square of
32
is less than
1025
by
1
.
Therefore, a perfect square will be obtained by subtracting
1
from the given number
1025
.
So, perfect square
=
1025
−
1
=
1024
Find the square root of 67.24 using long division method.
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0%
8.2
0%
8.3
0%
8.1
0%
8.4
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
↓
Quotient
↓
8.2
8
¯
67
.
¯
24
64
______
1.62
3.24
3.24
______
0
←
Remainder
√
67.24
=
8.2
Which least number must be subtracted to 899 to make a perfect square? (Use Long division method).
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0%
55
0%
56
0%
57
0%
58
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
↓
Quotient
↓
29
2
¯
8
¯
99
4
49
499
441
58
←
Remainder
The remainder is 58. it represents that the square of 29 is less than 899 by 58.
Therefore, a perfect square will be obtained by subtracting 58 from the given number 899.
So, perfect square = 899 - 58 = 841
Find the square root of 84.64 using long division method.
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0%
9.1
0%
9.2
0%
9.3
0%
9.4
A non-perfect square ends in 2, 3, 7 or ___.
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0%
4
0%
5
0%
0
0%
8
Explanation
A non-perfect square ends in 2, 3, 7 or 8.
Evaluate:
√
10
correct up to one place of decimal.
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0%
3.1
0%
3.16
0%
3.162
0%
3.1622
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Hence,
√
10
=
3.1
(correct upto one decimal place)
Estimate the square root of
500.
Report Question
0%
22.35
0%
20.3
0%
21.4
0%
23.6
Explanation
The two consecutive perfect squares among which
500
lies are
484
(
22
2
)
and
529
(
23
2
)
So, the whole number part of the square root of
500
is
22.
The decimal part can be determined by the formula:
Given number – Smaller perfect square
Greater perfect square – smaller perfect square
=
500
−
484
529
−
484
=
16
45
=
0.35
So, the estimated value of the square root of
500
by the approximation method is
22.35.
What is the square root of 506.25 using long division method?
Report Question
0%
22.5
0%
21.4
0%
23.4
0%
25.3
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
↓
Quotient
↓
22.5
2
¯
5
¯
06
.
¯
25
4
_______
42
106
84
_______
44.5
22.25
22.25
_______
0
←
Remainder
√
50.625
=
22.5
What is the square root of
292.41
using long division method?
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0%
17.1
0%
17.2
0%
17.3
0%
17.4
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Hence,
√
29.241
=
17.1
What is the square root of
156.25
using long division method.
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0%
12.3
0%
12.5
0%
12.4
0%
12.7
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
↓
Quotient
↓
12.5
1
¯
1
¯
56
.
¯
25
1
_______
22
56
44
_______
24.5
12.25
12.25
______
0
←
Remainder
√
156.25
=
12.5
Estimate the value of
√
750
.
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0%
24.3
0%
25.1
0%
23.2
0%
27.3
Explanation
27
2
= 729
28
2
= 784
In between this two squares, 750 is placed.
So average of
27
+
28
2
=
27.5
Then,
27.5
2
=
756.25
So,
√
750
≈
27.3
Find the approximate value of
√
5245
.
Report Question
0%
70.5
0%
72.3
0%
71.8
0%
79.2
Explanation
72
2
= 5184
73
2
= 5329
In between this two squares, 5245 is placed.
So average of
72
+
73
2
=
72.5
Then,
72.5
2
=
5256.25
So,
√
5245
≈
72.3
What is an approximate value of
√
9805
?
Report Question
0%
98.56
0%
97.23
0%
99.05
0%
100.34
Explanation
99
2
= 9801
100
2
= 10000
In between this two squares, 9805 is placed.
So the average of
99
+
100
2
=
99.5
Then,
99.5
2
=
9900.25
So,
√
9805
≈
99.05
Find the approximate value of
√
1235
.
Report Question
0%
35.15
0%
32.19
0%
30.25
0%
29.13
Explanation
35
2
= 1225
36
2
= 1296
In between this two squares, 1235 is placed.
So the average of
35
+
36
2
=
35.5
Then,
35.5
2
=
1260.25
So
√
1235
≈
35.15
What will be the units digit of the square of the given number
5125
?
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0%
0
0%
1
0%
5
0%
9
Explanation
Unit digit of multiplication of
2
numbers is obtained by taking the last digit of the multiplication of two numbers in the unit place
Units digit of
5125
×
5125
is obtained by taking the last digit of
5
×
5
=
25
⇒
Unit digit of square of
5125
is
5
.
What will be the unit's digit of the square of the given number
297
?
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0%
9
0%
7
0%
3
0%
1
Explanation
Unit's digit of multiplication of two numbers is obtained by taking the last digit of the multiplication of two numbers i.e. the digits at the unit place
Unit's digit of
297
×
297
is obtained by taking the last digits i.e.
7
×
7
=
49
⇒
Unit digit of square of
297
is
9
.
The number of prime factors of
36
is ____.
Report Question
0%
4
0%
3
0%
2
0%
1
Explanation
36
=
2
×
2
×
3
×
3
Clearly, only 2 and 3 are prime factors of 36.
Option C is correct.
Estimate the square root of
300
.
Report Question
0%
12.44
0%
16.66
0%
17.32
0%
18.54
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Incorrect : 0
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