MCQ Questions for Class 8 Maths Squares And Square Roots Quiz 5

What will be the unit digit of the square of 3853?

0%
3
0%
1
0%
7
0%
9

Explanation

Unit digit of

$3853$

$\rightarrow$

$3$

$3\times3$

$\rightarrow$

$9$

Hence, unit digit of

$3853\times3853$

$\rightarrow$

$9$

Hence, option D is correct.

What will be the unit digit of the square of the number

$81$ ?

0%
5
0%
7
0%
1
0%
3

Explanation

Unit digit of

$81$

$\rightarrow$

$1$

$1\times1$

$\rightarrow$

$1$

Hence, Unit digit of

$81\times81$

$\rightarrow$

$1$

Hence, Option C is correct.

What will be the unit digit of the square of 52698?

0%
4
0%
2
0%
9
0%
6

Explanation

Unit digit of

$52698$

$\rightarrow$

$8$

$8\times8$

$\rightarrow$

$64$

Hence, Unit digit of

$52698\times52698$

$\rightarrow$

$4$

Hence, Option A is correct.

What will be the unit digit of the square of 272?

0%
1
0%
4
0%
3
0%
8

Explanation

Unit digit of

$272$

$\rightarrow$

$2$

$2\times2$

$\rightarrow$

$4$

Hence, Unit digit of

$272\times272$

$\rightarrow$

$4$

Hence, Option B is correct.

What will be the unit digit of the square of 26837?

0%
4
0%
2
0%
9
0%
6

Explanation

Unit digit of

$26837$

$\rightarrow$

$7$

$7\times7$

$\rightarrow$

$49$

Hence, unit digit of

$26837\times26837$

$\rightarrow$

$9$

Hence, option C is correct.

What will be the unit digit of the square of 99880?

0%
2
0%
4
0%
6
0%
None of these

Explanation

Unit digit of

$99880$

$\rightarrow$

$0$

$0\times0$

$\rightarrow$

$0$

Hence, Unit digit of

$99880\times99880$

$\rightarrow$

$0$

Hence, Option D is correct.

What will be the unit digit of the square of 1234?

0%
3
0%
4
0%
5
0%
6

Explanation

Unit digit of

$1234$

$\rightarrow$

$4$

$4\times4$

$\rightarrow$

$16$

Hence, unit digit of

$1234\times1234$

$\rightarrow$

$6$

Hence, option D is correct.

The square of which of the following would be odd number ?

0%
$512$
0%
$320$
0%
$431$
0%
$220$

Explanation

The last digit of the square of

$431$ is

$1 (1 \times 1= 1),$ which forms an odd number

Also as we know that the square of any even digit will also be the even and square of any odd digit will also be the odd number

Hence, C will be correct answer.

Find the square root of the following number:

$1764$

0%
$42$
0%
$45$
0%
$49$
0%
$50$

Explanation

$1764=2\times 2\times 3\times 3\times 7\times 7=2^{2}\times 3^{2}\times 7^{2}=(2\times 3\times 7)^{2}$

By pairing the prime factor, then the square root of

$1764=$

$2\times 3\times 7$

$=42$

The square of which of the following would be an odd number ?

0%
$221$
0%
$226$
0%
$280$
0%
$232$

Explanation

The last digit of the square of

$221$ is

$1 (\text{because} \ 1 \times 1= 1),$ which forms an odd number.

Also as we know that the square of any even digit will also be the even and square of any odd digit will also be the odd number.

Hence, A will be correct answer.

What will be the unit digit of the square of 12796?

0%
6
0%
2
0%
1
0%
4

Explanation

Unit digit of

$12796$

$\rightarrow$

$6$

$6\times6$

$\rightarrow$

$36$

Hence, Unit digit of

$12796\times12796$

$\rightarrow$

$6$

Hence, Option A is correct.

446223 is obviously not a perfect square. Give reason.

0%
Last two digit is 23
0%
Number ends with 3
0%
Number starts with 44
0%
Data insufficient

Explanation

All the perfect square end with

$0,1,4,5,6,9$

Since

$446223$ ends with

$3$

Hence, it is not a perfect square.

Option B is correct.

What will be the unit digit of the square of 55555?

0%
4
0%
5
0%
0
0%
1

Explanation

Unit digit of

$55555$

$\rightarrow$

$5$

$5\times5$

$\rightarrow$

$25$

Hence, Unit digit of

$55555\times55555$

$\rightarrow$

$5$

Hence, Option B is correct.

The number which will end with digit

$1$ is _____.

0%
$(82)^2$
0%
$(97)^2$
0%
$(91)^2$
0%
none of these

Explanation

In option A, the last digit in the number $(82)^2$ is $4$

In option B, the last digit in the number $(97)^2$ is $9$

In option C, the last digit in the number $(91)^2$ is $1$

Therefore, option C is the correct answer.

Find the square of

$86$ .

0%
$5684$
0%
$7396$
0%
$6629$
0%
$3436$

Explanation

$(86)^{2}$

$\rightarrow$

$(80+6)^{2}$

$\rightarrow$

$(80)^{2}$

$+$

$(2\times80\times6)$

$+$

$(6)^{2}$

$(80+6)^{2}$

$\rightarrow$

$6400$

$+$

$960$

$+$

$36$

$(80+6)^{2}$

$\rightarrow$

$7396$

Hence, Option B is correct.

819027 is obviously not a perfect square. Give reason

0%
Last two digits are 27
0%
Number ends with 7
0%
Number starts with 8
0%
Data insufficient

Explanation

All the perfect square end with

$0,1,4,5,6,9$

Since

$819027$ ends with

$7$

Hence, it is not a perfect square.

Option B is correct.

Find the square root of 1024 by division method.

0%
42
0%
48
0%
38
0%
32

Explanation

$\therefore \sqrt{1024} = 32$

Find the square root of

$8100$ by the prime factorisation method.

0%
80
0%
90
0%
30
0%
70

Explanation

$8100$ can be written as

$5\times5\times3\times3\times3\times3\times2\times2$ .

To find the square root, we will write it as

$5\times3\times3\times2$ which is

$90$ .

Hence square root of

$8100$ is

$90$ .

Find the square root of the

$9216$ by the prime factorisation method.

0%
96
0%
86
0%
106
0%
76

Explanation

$9216= 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3=2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 3^{2}=(2\times 2\times 2\times 2\times 2\times 3)^{2}$

By pairing the prime factor, then

The square root of

$9216=$

$2\times 2\times 2\times 2\times 2\times 3$

$=96$

Find the square root of 15129 by the division method.

0%
117
0%
107
0%
123
0%
127

Find the square root of the following number by division method.
3481

0%
71
0%
61
0%
51
0%
59

Find the square root of

$576$ by division method.

0%
36
0%
24
0%
34
0%
46

Find the square root of the following number by division method:
4489

0%
63
0%
67
0%
73
0%
77

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

$(i) 402, (ii) 1989, (iii) 3250, (iv) 825, (v) 4000$

0%
$(i) 2, (ii) 22, (iii) 1, (iv) 21, (v) 52$

Square root of the perfect square:
$(i) 20, (ii) 34 ,(iii) 55, (iv) 26, (v) 67$
0%
$(i) 2, (ii) 53, (iii) 1, (iv) 41, (v) 31$

Square root of the perfect square:
$(i) 20, (ii) 44, (iii) 57, (iv) 28, (v) 63$
0%
$(i) 6, (ii) 22, (iii) 50, (iv) 31, (v) 40$

Square root of the perfect square:
$(i) 19, (ii) 41, (iii) 49 ,(iv) 27 ,(v) 65$
0%
$(i) 8, (ii) 41, (iii) 12, (iv) 56, (v) 4$

Square root of the perfect square:
$(i) 19 ,(ii) 22, (iii) 37, (iv) 26, (v) 61$

Explanation

For

$402$

Nearest perfect square is

$400$

$\sqrt{400}$

$=$

$20$

$402$

$-$

$400$

$=$

$2$

For

$1989$

Nearest perfect square is

$1936$

$\sqrt{1936}$

$=$

$44$

$1936$

$-$

$1989$

$=$

$53$

For

$3250$

Nearest perfect square is

$3249$

$\sqrt{3249}$

$=$

$57$

$3250$

$-$

$3249$

$=$

$1$

For

$825$

Nearest perfect square is

$784$

$\sqrt{784}$

$=$

$28$

$825$

$-$

$784$

$=$

$41$

For

$4000$

Nearest perfect square is

$3969$

$\sqrt{3969}$

$=$

$63$

$4000$

$-$

$3969$

$=$

$31$

From this, Option B is correct answer.

Find the square root of

$3136$ by division method.

0%
56
0%
66
0%
46
0%
36

Explanation

$\therefore \sqrt{3136} = 56$

Find square root of 8281.

0%
41
0%
71
0%
91
0%
111

Explanation

$\therefore \sqrt{8281} = 91$

Find the smallest number by which

$9408$ must be divided so that the quotient is a perfect square. Find the square root of the quotient.

0%
Smaller number: $5$ , Quotient: $3036$ , Square root: $54$ .
0%
Smaller number: $3$ , Quotient: $3136$ , Square root: $56.$
0%
Smaller number: $7,$ Quotient: $3236$ , Square root: $57.$
0%
Data insufficient

Explanation

We have 9408=

$\displaystyle \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times 3\times \underline{7\times 7}$
If we divide 9408 by the factor 3 then

$\displaystyle 9408\div 3=3136=\underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{7\times 7}$ which is a perfect square (because

$3136 = (56)^2$ )
And

$\displaystyle \sqrt{3136}=2\times 2\times 2\times 7=56$

Find a Pythagorean triplet in which one member is 12

0%
5, 12, 13
0%
7, 12, 19
0%
11, 12, 15
0%
11, 12, 18

Explanation

If we take m

$\displaystyle ^{2}$ -1=12
Then m

$\displaystyle ^{2}$ =12+1=13
Then the value of m will not be an integer
So we try to take

$m^{2}+1=12\ Again\ m \displaystyle ^{2}=11$ will not give an integer value for m
So let us take 2m = 12
then m=6
Thus

$\displaystyle m^{2}-1=36-1=35$ and

$\displaystyle m^{2}+1=36+1=37$
Therefore the required triplet is 12, 35, 37
Note : All Phythagorean triplets may not be obtained using this form For example another triplet 5, 12, 13 also has 12 as a member

Find the square root of : (i)

$729$ (ii)

$1296$

0%
$13, 36$
0%
$27,36$
0%
$17, 16$
0%
$23, 26$

Explanation

Prime factorization of

$729$ is

$729=3\times 3\times 3\times 3\times 3\times 3=3^6$

Prime factorization of

$1296$ is

$1296=2\times 2\times 2 \times 2\times 3\times 3\times 3\times 3=2^4\times 3^4$

$\sqrt{729}=\sqrt{3^6}=3^3=27$

$\sqrt{1296}=\sqrt{2\times2\times 2\times 2\times 3\times 3\times 3\times 3}=2\times 2\times 3\times 3=36$

Find the square root of 6400.

0%
70
0%
80
0%
60
0%
90

Explanation

Write 6400=

$\displaystyle \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times \underline{5\times 5}$
Therefore

$\displaystyle \sqrt{6400}=2\times 2\times 2\times 2\times 5=80$

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 5 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 5 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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