Squares And Square Roots- 1 - Free MCQ Practice Test with solutions, UPSC

A perfect square is a number that can be written as the square of a whole number.
Using Property:
A perfect square number can only end in 0, 1, 4, 5, 6, or 9
It can never end in 2, 3, 7, or 8.

Now check each option:

• a) 222222 → ends in 2 → NOT a perfect square
• b) 23453 → ends in 3 → NOT a perfect square
• c) 1681 → ends in 1 → MAY be a perfect square (possible)
• d) 1057 → ends in 7 → NOT a perfect square

Only 1681 has a correct unit digit.

And we know:
41 × 41 = 1681

Correct Option: C

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.

Option 1:
√576 = 24

Option 2:
√841 = 29

Option 3:
√778 = 27.89 It is not perfect square

Option D:
√529 = 23

Hence, the answer is option C.

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.

169 = 13 × 13, so it is a perfect square. The other numbers cannot be expressed as the square of a whole number.

12² = 12*12 = 144

13² = 13*13 = 169

Now numbers are between144 and 169 are:

145, 146, 147,.............168

Total number = 24

So total numbers lies between 144 and 169 is 24

When squaring the number 5278, the unit digit is determined by the square of the unit digit of the original number.

Since the unit digit of 5278 is 8, squaring it gives 8 × 8 = 64.

Therefore, the unit place digit of 5278² is 4.
Therefore correct answer : Option A

180 = 2² × 3² × 5. To make all powers even, multiply by 5.
180 × 5 = 900 = 30²