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Squares And Square Roots Test - 7

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Squares And Square Roots Test - 7

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Question 1
1 / -0

Find the value of x in the given equation.

A
12,250

B
35,536

C
45,520

D
65,536

Solution

Squaring both sides, we get

Now, again squaring both sides, we get

x = 65,536
Question 2
1 / -0

What is the simplified form of ?

A

B

C

D

Solution

=

=

=

=

=
Question 3
1 / -0

_{= x, then the value of x is}

A
0.34

B

C

D
0.06

Solution

= x

0.09 + 0.25 = x²x =
Question 4
1 / -0

If , then x is equal to

A
5

B
3

C
2

D
4

Solution
Question 5
1 / -0

Which among the following can definitely not be a square number?

A
16384

B
13689

C
28561

D
48542

Solution

Square numbers always end with digits 0, 1, 4, 5, 6, 9.
So, from looking at the units digits in the given options, we can say that only 48542 can definitely not be a square number.
Question 6
1 / -0

A Google employee's age is multiplies by times itself and then 10 is subtracted from the product obtained. If the final result is 4490, then the age is________.

A
70

B
60

C
50

D
40

Solution

Suppose 'a' be the age of Google company employee's
Then according to the question,
Question 7
1 / -0

The product of two numbers is 4,55,625. If one number is 9 times the other, find the numbers.

A
75 and 2015

B
110 and 2050

C
125 and 1025

D
225 and 2025

Solution

Let the first number be x; then the other number will be 9x.
So, x(9x) = 4,55,625
9x² = 4,55,625
x² = 50,625
x =
x = 225
Hence, the numbers are 225 and 2025.
Question 8
1 / -0

What is the smallest number by which 7776 must be divided to get a perfect square?

A
6

B
2

C
3

D
1

Solution

7776 =
Since two digits (2 and 3) are not in pairs, the smallest number by which 7776 must be divided to get a perfect square is 2 x 3 = 6
Question 9
1 / -0

What is the square root of 10.24?

A
0.32

B
3.2

C
4.2

D
0.42

Solution

We will find the square root of 10.24 by long division method.

Square root of 10.24 = 3.2
Question 10
1 / -0

What is the value of 100² - 99²by observing the given pattern?

2² - 1² = 2 + 1
3² - 2² = 3 + 2

A
199

B
100

C
99

D
88

Solution

2² - 1² = 2 + 1
3² - 2² = 3 + 2
100² - 99² = 100 + 99 = 199
Question 11
1 / -0

The ratio of the marks of four students is 2 : 3 : 5 : 6, such that the sum of their squares is 10,656. Find the marks of the four students, respectively.

A
6, 9, 15 and 36

B
12, 18, 30 and 36

C
24, 36, 60 and 72

D
48, 72, 120 and 144.

Solution

The given ratio is 2 : 3 : 5 : 6.
So, let the marks be 2x, 3x, 5x and 6x.
(2x)² + (3x)² + (5x)² + (6x)² = 10,656
4x² + 9x² + 25x² + 36x² = 10,656
74x²= 10,656
x²= 10656 ÷ 174
x²= 144
x = 12
The marks of the students are 24, 36, 60 and 72, respectively.
Question 12
1 / -0

The value ofis ______.

A
1.34

B
2.84

C
3.04

D
4.54

Solution

= 1.34 (approx.)
Question 13
1 / -0

What do we need to subtract from 99,999 to make it a perfect square?

A
43

B
58

C
256

D
143

Solution

We need to subtract 143 from 99,999 to make it a perfect square.
99,999 - 143 = 99,856, which is the square of 316.
Question 14
1 / -0

Find the value of .

A
0.04

B
0.54

C
0.94

D
1.94

Solution
Question 15
1 / -0

Find the respective square roots of the following numbers up to two decimal places:

2.8 and 3.6

A
1.67 and 1.89

B
1.07 and 1.09

C
0.60 and 0.87

D
2.67 and 3.89

Solution
Question 16
1 / -0

What will be the length of a square field if its area is given as ?

A
2.69 m

B
3.56 m

C
4.5 m

D
5.43 m

Solution

Let the length of the field be x.
Area of the field =
=
=

x = 4.5 m (approx.)
Question 17
1 / -0

The total fee of all students in a hostel is Rs. 48,672. Each student's fee is one half of the number of students. What is the total number of students in the hostel?

A
312

B
345

C
376

D
394

Solution

Let the total number of students be x.
Each student's fee is half the number of students.
According to the question,

x² = 97344
x = 312
So, the number of students in the hostel is 312.
Question 18
1 / -0

In a school assembly, the students are arranged in rows to form a perfect square; but in doing so, 25 students are left out. If the total number students is 1181, find the number of students in each row.

A
30

B
34

C
36

D
38

Solution

Total students who form a square:
1181 - 25 = 1156
Let the number of rows be x.
So, x × x = 1156
x² = 1156
x = 34
Number of students in each row = 34
Question 19
1 / -0

A trust collects as many paise from each member of the trust as the number of members. If the total collection is Rs. 29.16, then what is the number of members in the trust?

A
54

B
55

C
56

D
57

Solution

Let the number of members in the trust be x.
Then, amount received from each member = x paise
Now, total collection = x² paise
x² = (29.16 × 100)
x =
x = 54
So, the number of members in the trust is 54.
Question 20
1 / -0

A charitable trust wants to fence a square plot whose area is given as 6448.09 sq. m. What is the side of the plot?

A
89.2 m

B
85.7 m

C
82.5 m

D
80.3 m

Solution

Side of the plot = = 80.3 m
Question 21
1 / -0

Find the value of .

A
4.84

B
4.69

C
4.89

D
6.03

Solution

=

=

=

=

= 5 - 0.16

= 4.84
Question 22
1 / -0

Find the values of P, Q, R and S.

i) The square root of 1002001 is P .
ii) The square root of 2450.25 is Q .
iii) The square root of 8445.61 is R .
iv) The square of 58 is S .

A
P is 1001, Q is 49.5, R is 47.9, and S is 3364.

B
P is 1001, Q is 49.5, R is 91.9, and S is 3364.

C
P is 1001, Q is 33.5, R is 91.9, and S is 3364.

D
P is 1002, Q is 49.5, R is 91.8, and S is 3364.

Solution

For P: = 1001

For Q: = 49.5

For R: = 91.9

For S: Square of 58 = 3364
Question 23
1 / -0

Which of the following statements is/are true?

A
A number having 2, 3, 7, or 8 at the ones place is never a perfect square; in other words, no square number ends in 2, 3, 7, or 8.

B
The square of a natural number other than 1 is either a multiple of 4 or exceeds a multiple of 4 by 1 .

C
Squares of even numbers are always even numbers and square of odd numbers are always odd.

D
All of these

Solution

(1) A number having 2, 3, 7, or 8 at the ones place is never a perfect square; in other words, no square number ends in 2, 3, 7, or 8.
Example: None of the numbers 152, 7693, 14357, 88888 and 798328 is a perfect square because the unit digit of each number is 2, 3, 7, or 8.

(2) The square of a natural number other than 1 is either a multiple of 4 or exceeds a multiple of 4 by 1.
Example: 67, 146 and 10003 are not perfect squares as they leave respectively the remainders of 3, 2 and 3 when divided by 4.

(3) Squares of even numbers are always even numbers and square of odd numbers are always odd.
Example: 12²= 12 × 12 = 144 (both are even numbers)
19²= 19 × 19 = 361 (both are odd numbers)
Question 24
1 / -0

Consider the following statements and mark the correct option accordingly.

Statement I: The unit digit of the square of a natural number is the unit digit of the square of the digit at the ones place of the given natural number.
Statement II: The square of a number n is equal to the sum of first n odd natural numbers.

A
Only statement II is true.

B
Both statement are false.

C
Both statements are true.

D
Only statement I is true.

Solution

Statement I: The unit digit of the square of a natural number is the unit digit of the square of the digit at the ones place of the given natural number.
For example, let's find out the unit digit of the square of (i) 146 and (ii) 321.
Solution:
(i) Since the unit digit of 6²= 36 is 6, the unit digit of the square of 146 is 6.
(ii) Since the unit digit of 1²= 1 is 1, the unit digit of the square of 321 is 1.

Statement II: The square of a number n is equal to the sum of first n odd natural numbers.
1²= 1
2²= 1 + 3
3³ = 1 + 3 + 5
4² = 1 + 3 + 5 + 7, and so on.
So, both statements are true.
Question 25
1 / -0

State true (T) or false (F) for the following statements.

i) If a number has 3 or 7 at the ones place, then its square ends in 9.
ii) 33.5² lies between 500 and 1000.
iii) If a number has 5 at the ones place, then its square ends in 5.
iv) The area of a square, whose side is 8 cm, is 64 cm².

A
i) - T, ii) - F, iii) - T, iv) - T

B
i) - T, ii) - F, iii) - T, iv) - F

C
i) - T, ii) - F, iii) - F, iv) - T

D
i) - F, ii) - F, iii) - T, iv) - T

Solution

i) If a number has 3 or 7 at the ones place, then its square ends in 9.
E.g. 33² = 1089, 17²= 289, 13² = 169
So, statement (i) is true.
ii) 33.5²= 1122.25; it does not lie between 500 and 1000. So, statement (ii) is false.
iii) If a number has 5 in the ones place, then its square ends in 5.
E.g. 5²=25, 15²=225, 25²= 625
So, statement (iii) is true.
iv) The area of a square, whose side is 8 cm, is 64 cm².
8 × 8 =
So, statement (iv) is true.

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