Squares and Square Roots Test

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Squares and Square Roots Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

Find the square root of the following number:
$$1764$$

A
$$42$$

B
$$45$$

C
$$49$$

D
$$50$$

Solution

$$1764=2\times 2\times 3\times 3\times 7\times 7=2^{2}\times 3^{2}\times 7^{2}=(2\times 3\times 7)^{2}$$
By pairing the prime factor, then the square root of
$$1764=$$ $$2\times 3\times 7$$ $$=42$$
Question 2
1 / -0

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

A
$$221$$

B
$$226$$

C
$$280$$

D
$$232$$

Solution

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.
Question 3
1 / -0

446223 is obviously not a perfect square. Give reason.

A
Last two digit is 23

B
Number ends with 3

C
Number starts with 44

D
Data insufficient

Solution

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.
Question 4
1 / -0

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

A
4

B
5

C
0

D
1

Solution

Unit digit of $$55555$$ $$\rightarrow$$ $$5$$
$$5\times5$$ $$\rightarrow$$ $$25$$
Hence, Unit digit of $$55555\times55555$$ $$\rightarrow$$ $$5$$
Hence, Option B is correct.
Question 5
1 / -0

Find the square of $$86$$.

A
$$5684$$

B
$$7396$$

C
$$6629$$

D
$$3436$$

Solution

$$(86)^{2}$$ $$\rightarrow$$ $$(80+6)^{2}$$
$$(80+6)^{2}$$ $$\rightarrow$$ $$(80)^{2}$$ $$+$$ $$(2\times80\times6)$$ $$+$$ $$(6)^{2}$$
$$(80+6)^{2}$$ $$\rightarrow$$ $$6400$$ $$+$$ $$960$$ $$+$$ $$36$$
$$(80+6)^{2}$$ $$\rightarrow$$ $$7396$$
Hence, Option B is correct.
Question 6
1 / -0

819027 is obviously not a perfect square. Give reason

A
Last two digits are 27

B
Number ends with 7

C
Number starts with 8

D
Data insufficient

Solution

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.
Question 7
1 / -0

Find the square root of 1024 by division method.

A
42

B
48

C
38

D
32

Solution

$$\therefore \sqrt{1024} = 32$$
Question 8
1 / -0

Find the square root of $$8100$$ by the prime factorisation method.

A
80

B
90

C
30

D
70

Solution

$$8100$$ 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 $$90$$.
Question 9
1 / -0

Find the square root of the $$9216$$ by the prime factorisation method.

A
96

B
86

C
106

D
76

Solution

$$9216= 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3=2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 3^{2}=(2\times 2\times 2\times 2\times 2\times 3)^{2}$$
By pairing the prime factor, then
The square root of $$9216=$$ $$2\times 2\times 2\times 2\times 2\times 3$$ $$=96$$
Question 10
1 / -0

Find the square root of 15129 by the division method.

A
117

B
107

C
123

D
127

Solution

We will use long division method
In this, first group the numbers into two starting from unit place, these groups are called periods.
Use the largest number whose square is equal or less than the first period number
Subtract the product of divisor and quotient from the first period and bring down the second period to the right of remainder. This will become new divident.
In this way we can find out the square root .
Hence, Option C is correct.

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Squares and Square Roots Test - 19

Result

Squares and Square Roots Test - 19

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SHARING IS CARING

Question 1

$$42$$

$$45$$

$$49$$

$$50$$

Solution

Question 2

$$221$$

$$226$$

$$280$$

$$232$$

Solution

Question 3

Last two digit is 23

Number ends with 3

Number starts with 44

Data insufficient

Solution

Question 4

4

5

0

1

Solution

Question 5

$$5684$$

$$7396$$

$$6629$$

$$3436$$

Solution

Question 6

Last two digits are 27

Number ends with 7

Number starts with 8

Data insufficient

Solution

Question 7

42

48

38

32

Solution

Question 8

80

90

30

70

Solution

Question 9

96

86

106

76

Solution

Question 10

117

107

123

127

Solution

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