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Squares And Square Roots Test - 6

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Squares And Square Roots Test - 6

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Question 1
1 / -0

Find the value of x in .

A
1

B
4

C
9

D
25

Solution

3 + = 4
= 1

x = (1)²

x = 1

Option (1) is correct.
Question 2
1 / -0

Find the value of u if u = ^.

A
4.2

B
8

C
4.6

D
6

Solution

u = u =
u = = 4.2
Option (1) is correct.
Question 3
1 / -0

Find the least number which must be added to 9569 to make it a perfect square.

A
35

B
25

C
49

D
53

Solution

So, to form a perfect square 35 need to be added.
Option (1) is correct.
Question 4
1 / -0

Find the value of x in .

A
4

B
5

C
6

D
7

Solution

17 = 13 + x
17 - 13 = x
x = 4
Option (1) is correct.
Question 5
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 6
1 / -0

A number is multiplied by times itself and then, 98 is added to it. If the final result is 1250, then the number is

A
18

B
26

C
16

D
22

Solution

Let the number be Y.
Also, times of Y is represented by Y or _.

According to information given in the question, we get

+ 98 = 1250
1152 =
= 1152
= 324

Y = 18

Option (1) is correct.
Question 7
1 / -0

Product of two numbers is 2925. If one number is 13 times the other, then find one of the numbers.

A
15

B
16

C
17

D
18

Solution

Let the first number be x.
Then, the other number will be 13x.

According to the information given in the question, we get

= 2925

= 2925

=
= 225

x = 15

Option (1) is correct.
Question 8
1 / -0

The least positive integer with which 771.75 is multiplied to get a perfect square, is

A
7

B
6

C
5

D
4

Solution

We have

=

So, the least positive integer with which 771.75 should be multiplied to make it a perfect square, is 7.
Option (1) is correct.
Question 9
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 10
1 / -0

The value of is

A
8

B
9

C
7

D
None of these

Solution

We have,

=

=

= 8

Option (1) is correct.
Question 11
1 / -0

Boxes A, B and C have candies in the ratio 1 : 2 : 3 and the sum of their squares is 1400. Find how many candies are there in box B.

A
20

B
25

C
30

D
35

Solution

Let the number of candies in boxes A, B and C be x, 2x and 3x, respectively.
They are in the ratio 1 : 2 : 3.
As per the information given in the question,

x² + 4x² + 9x² = 1400
14x² = 1400
x = 10

So, candies in boxes A, B and C are 10, 20 and 30, respectively.
So, candies in box B = 20

Option (1) is correct.
Question 12
1 / -0

Directions: Find the value of .

A

B

C

D

Solution

We have,

=

=

=

Option (1) is correct.
Question 13
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 14
1 / -0

Directions: Solve .

A

B

C

D

Solution

We have,

=

=

=
=

Option (1) is correct.
Question 15
1 / -0

Directions: Find the square root of following up to two decimal places.

I.

II.

A
(I) 2.67
(II) 2.74

B
(I) 2.67
(II) 2.93

C
(I) 2.90
(II) 2.74

D
(I) 3.12
(II) 4.23

Solution

= = = = 2.67

= = = 2.74

Option (1) is correct.
Question 16
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 17
1 / -0

A single insect in a cage, on an average, eats feed (in grams) half of what it weighs. If total weight is 0.8 kg, then find the average weight of the insect.

A
40 g

B
25 g

C
30 g

D
35 g

Solution

Total weight = 0.8 kg = 800 g

Feed weight =

Insects weight = x
According to the question,
= 800

x² = 1600
x = 40
Average weight of insect = 40 g
Option (1) is correct.
Question 18
1 / -0

Anamika was arranging cakes in rows to form a perfect square and while she was doing that, 41 cakes were left out. The total number of cakes was 12141. How many cakes were in a row?

A
110

B
121

C
131

D
141

Solution

Total number of cakes = 12141
Number of cakes left out = 41
Total number of cakes arranged = 12100
Let the number of cakes in row = x
x² = 12100
x = 110
Option (1) is correct.
Question 19
1 / -0

A principal wished to arrange his students, who were 1943 in number, in the form of a square and found that there were 7 students left over. How many students were there in each row?

A
32

B
36

C
44

D
40

Solution

Let the number of students in each row be a.
Then, number of rows = a
∴ Number of students in 'a' rows = a × a = a²
It is given that after arranging the students in a square, 7 students were left over.
∴ Total number of students = a² + 7
But the total number of students is 1943.
Or a² = 1943 - 7
Or a² = 1936
Or a = Or a =
Or a = 11 × 2 × 2
Or a = 44
Thus, there were 44 students in each row.
Question 20
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 21
1 / -0

Directions: Find the value of .

A

B

C

D

Solution

=
=

=

=

=

=

=

Option (1) is correct.
Question 22
1 / -0

Directions: Find the values of A, B, C and D.

(i) Square root of 123.21 is A.
(ii) Square root of 655.36 is B.
(iii) Square root of 4747.21 is C.
(iv) Square root of 552.25 is D.

A
A = 11.1, B = 25.6, C = 68.9, D = 23.5

B
A = 12.5, B = 25.6, C = 16.5, D = 23.5

C
A = 11.1, B = 25.6, C = 18.5, D = 19.5

D
A = 12.8, B = 17.87, C = 16.9, D = 12.3

Solution

Square root of A (123.21) is 11.1.

Square root of B is 25.6.

Square root of C is 68.9.

Square root of D (552.25) is 23.5.
Option (1) is correct.
Question 23
1 / -0

Which of the following statements is true?

A
The square of numbers is always even.

B
There are 2n + 1 non perfect square numbers between the squares of the numbers n and (n + 1).

C
The sum of 1 + 3 + 5 + 7 + ....upto 15 terms is 225.

D
All of the above

Solution

(1) The square of numbers is always even.
This statement is false. Example: Square of 5 is 25, which is not an even number.

(2) There are 2n non perfect square numbers between the squares of the numbers n and (n + 1) and not 2n + 1.
False statement.

(3) The sum of 1 + 3 + 5 + 7 + ....upto 15 terms is 225.
This is a true statement.
The sum of 1 + 3 + 5 + 7 + ....upto n terms is n².
So, 1 + 3 + 5 + 7 + ...upto 15 terms = 15² = 225.
Question 24
1 / -0

Directions: Study the statements carefully and choose the correct option.

Statement 1: If a natural number can be expressed as a sum of successive odd natural numbers starting with 1, then it is a perfect square.
Statement 2: Each and every square number has even number of factors.

A
Only statement 1 is true

B
Only statement 2 is true

C
Both statements are true

D
None of these is true

Solution

(Statement 1):
If a natural number can be expressed as a sum of successive odd natural numbers starting with 1, then it is a perfect square.
For example:

1 + 3 + 5 = 3²
1 + 3 + 5 + 7 = 4²
1 + 3 + 5 + 7 + 9 = 5²
So, statement (1) is true.

(Statement 2): Each and every square number has even number of factors.
For example:

2² has 3 factors(1,2 and 4)
3² has 3 factors(1,3 and 9)
2² x 5² has 9 factors(1,2 4,5 ,10, 20, 25, 50 and 100)

So, statement (2) is false.
Question 25
1 / -0

Directions: State T for true or F for false.

I. The square root of 0.4 is 0.2.
II. There are 313 natural numbers between 156² - 157².
III. Negative numbers have positive square numbers.
IV. Sum of first n odd natural numbers is n².

A
I - F, II - F, III - T, IV - T

B
I - T, II - F, III - T, IV - T

C
I - F, II - T, III - T, IV - T

D
I - T, II - T, III - T, IV - F

Solution

I. The square root of 0.4 is 0.632.
So, statement (I) is false.

II. There are 312 natural numbers between 156² - 157²
So, statement (II) is false.

III. (-3)² = 9 is a positive number.
So, statement (III) is true.

IV. Sum of first n odd natural numbers is n².
So, statement (IV) is true.

Option (1) is correct.

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