Test: Squares And Square Roots- 1

QUESTION: 1

Which of the following is a perfect square number?

A.
222222
B.
23453
C.
1681
D.
1057

Solution: The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.

QUESTION: 2

Which of the following would end with digit 1?

A.
123²
B.
161²
C.
77²
D.
82²

Solution: Option B is correct because the unit digit of 161 is 1 and if unit digit of any digit ends with 1 the its square will also end with 1.

QUESTION: 3

Without adding, find the sum. 1 + 3 + 5 + 7 + 9

A.
16
B.
36
C.
9
D.
25

Solution:

Here, we have to find the sum of first five odd natural numbers.

Therefore, 1 + 3 + 5 + 7 + 9 = (5)2 = 25

QUESTION: 4

Find the smallest whole number by which 1008 should be multiplied to get a perfect square number .

A.
8
B.
7
C.
2
D.
5

Solution:

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now 1008×7= 7056

=2×2×2×2×3×3×7×7

So, the square root will be =2×2×3×7 = 84

QUESTION: 5

When a square number ends in _______, the number whose square it is, will have either 4 or 6 in unit’s place.

A.
2
B.
3
C.
6
D.
0

Solution: Answer is 6 because the last digit of the square of 4 is 6 and 4 is also 6.

QUESTION: 6

Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.

A.
136
B.
8
C.
9
D.
64

Solution:

QUESTION: 7

Find the perfect square numbers between 30 and 40.

A.
36
B.
49
C.
25
D.
none of these

Solution:

Since, 1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

Thus, 36 is a perfact square number between 30 and 40.

QUESTION: 8

All square numbers end with __________ at unit’s place.

A.
1
B.
9
C.
0
D.
0, 1, 4, 5, 6 or 9

Solution:

The numbers ending with 0 gives 0,numbers ending with 1,9 gives 1, numbers ending with 2,8 gives 4, numbers ending with 3,7 gives 9, numbers ending with 5 gives 5 and numbers ending with 4,6 gives 6. Hence we get only 0,1,4,5,6,9 at the unit's place.

QUESTION: 9

Without doing any calculation, find the numbers which are surely perfect squares.