Squares and Square Roots Test

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Squares and Square Roots Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers is definitely not a perfect square?

A
960400

B
23235722

C
23338561

D
1046529

Solution

If a number is a perfect square, it must end with 0, 1, 4, 9, 6 or 5.
23235722 ends with 2.
So, 23235722 can never be a perfect square.
Question 2
1 / -0

If one of the numbers in the Pythagorean triplet is 35, then which of the following triplets is correct?

A
13, 35, 37

B
14, 35, 38

C
12, 35, 36

D
12, 35, 37

Solution

Let m² - 1 = 35
∴ m² = 36
m = 6
So, 2m = 2 ×6 = 12
m² + 1 = 37
So, required Pythagorean triplet = 12, 35, 37
Hence, answer option 4 is correct.
Question 3
1 / -0

Which of the following is the smallest number that should be subtracted from 549162 in order to make it a perfect square?

A
36

B
62

C
81

D
24

Solution

81 must be subtracted from 549162 to make it a perfect square.
Question 4
1 / -0

Which of the following is the smallest square number, which is divisible by 66, 99 and 154?

A
(461)²

B
(462)²

C
(322)²

D
(576)²

Solution

We need to find the LCM of 66, 99 and 154.
LCM = 2 3 11 3 7
This is not a perfect square.
We multiply it by 11 7 2 to make it a perfect square.
Reguired square number = 2 2 3 3 7 7 11 11
= (2 3 7 11)²
= (462)²
Question 5
1 / -0

Sonia and Ravi have the same amount of money. If the product of their amounts (in rupees) is 6084, then how much money does Sonia have?

A
Rs. 68

B
Rs. 86

C
Rs. 78

D
Rs. 88

Solution

Let the amount of money (in rupees) with Sonia = x
Then, the amount of money (in rupees) with Ravi = x
∴ Product of their amounts = x² = 6084
Square Root of 6084 is 78
Amount of money with Sonia = Rs. 78
Question 6
1 / -0

What will be the number of zeros (at the end) in the squares of the following numbers, respectively?

720, 93600 and 731000

A
1, 2 and 3

B
2, 3 and 6

C
2, 4 and 6

D
2, 4 and 4

Solution

The number of zeros gets doubled after squaring a number.
∴ (720)² will have 2 zeros.
(93600)² will have 4 zeros.
(731000)² will have 6 zeros.
Question 7
1 / -0

If a = 2 and b = 4, then what is the value of ?

A
4

B
5

C
6

D
7

Solution

= 4
Question 8
1 / -0

The floor of Dany's rectangular living room is 12 m long and 5.5 m wide. He has a square rug that covers of the area of the floor. What is the length of each side of the square rug?

A
5.1 m

B
5.2 m

C
5.3 m

D
5.4 m

Solution

Area of the floor of the room = 12 × 5.5 = 66 m²
Area of the square rug = = 28.3 m²
Length of each side of the square rug = = 5.3 m
Question 9
1 / -0

If the radius of a circle is cm, then find the area of the circle.

A
23.79 cm²

B
31.36 cm²

C
37.76 cm²

D
47.1 cm²

Solution

Area of the circle =
= 3.14
= 3.14 15
= 47.1 cm²
Question 10
1 / -0

The square of the number '74' when added to the square of the number 'x' gives 9320 as the result. What is the value of 'x'?

A
58

B
62

C
64

D
68

Solution

x² + 74² = 9320
x² = 9320 - 74²
= 9320 - 5476 = 3844
x = = 62
Question 11
1 / -0

What is the value of ^?

A
7

B
2

C
9

D
5

Solution

Hence, answer option 1 is correct.
Question 12
1 / -0

Which of the following is the same as ?

A
40²

B
120²

C
43²

D
40² + 3²

Solution

Option (3) is correct.
Question 13
1 / -0

If it is given that 1 + 3 + 5 = 3² and 1 + 3 + 5 + 7 = 4², then what will be the value of 7 + 9 + 11 + ................ + 99?

A
50² - 3²

B
50² + 3²

C
50² - 13²

D
50²

E
None of these

Solution

It is given that 1 + 3 + 5 = 3² as there are 3 odd numbers.
And 1 + 3 + 5 + 7 = 4² as there are 4 odd numbers.
Then, 1 + 3 + 5 + 7 + .......... + 99 = 50² as there are 50 odd numbers.
But we need to find the value of 7 + 9 + 11 + 13 ......... + 99.
So, we need to subtract 1 + 3 + 5 from 50² to get the required value.
Thus, the answer is 50² - 3².
Question 14
1 / -0

Solve: (144)^-1/2 x (144)² x (1/1296)^1/2 x (2304)^-1/2

A
144

B
12

C
1

D
(- 4)

Solution

Solve the given expression step by step.
(144)^-1/2 = 1/(144)^1/2
= 1/12
144²= 12⁴
(1/1296)^1/2 = 1/36
(2304)^-1/2 = 1/( 2304)^1/2
= 1/48
So, the value of the required expression is:
(1/12) x 12⁴ x (1/36) x (1/48) = 1
Question 15
1 / -0

What is the simplified form of ?

A
22

B
30

C
8

D
14

Solution

22 - 8 = 14