Content Curator
The Square of any number is the product of the number with itself. Let's suppose we want to calculate the square of 2, then the square of 2 will be 2x2, i.e., 4. We can calculate the square of any number by simply multiplying it with itself. Calculating the square root of any number is the reverse process of squaring. In this section, we will cover the square and square roots of numbers and important MCQ questions from this section.
Also read: Properties of Determinants
Square of a number
Any natural number m represented as n² can be termed as a ‘Square’ number, where n is also a natural number. For more understanding, consider an example. 25 is a square number as it can be expressed as (5) 2.
Similarly, we check whether 40 is a square number or not.
A square number less than 40 is 36= 6*6 and the next square number is 49=7*7.
Hence, 40 is not a square number.
Also read: Quadrilateral Formula
Examples for Square of number
The first 10 Square numbers are mentioned in the table given below. You can similarly calculate the square of any number.
| Number | Square Number |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
Square Root of a number
The Square root of a number is the inverse of the square of that number. Let us understand the square root of a number with the help of an example.
The square root of 4 is 2. 4 can be expressed as 2*2 or (2)2. Similarly, the square root of 36 is 6.
Also read: First Order Differential Equation
Examples for Square Root of a number
The first 10 Square Roots are mentioned in the table given below. You can similarly calculate the square root of any number.
| Number | Square Root |
|---|---|
| 1 | 1 |
| 4 | 2 |
| 9 | 3 |
| 16 | 4 |
| 25 | 5 |
| 36 | 6 |
| 49 | 7 |
| 64 | 8 |
| 81 | 9 |
| 100 | 10 |
| 121 | 11 |
| 144 | 12 |
| 169 | 13 |
| 196 | 14 |
| 225 | 15 |
| 256 | 16 |
| 289 | 17 |
| 324 | 18 |
| 361 | 19 |
| 400 | 20 |
Square and Square Roots Important MCQs
Question 1. What will be at the unit place if 4238 is squared?
Click here for the answer
Answer. 4
Explanation: 8 is at the unit place and the square of 8 is 64. Hence, 4 is the unit place of the square.
Question 2. Which number is a perfect square from the given numbers?
6928, 40, 625, 1028, 1148, 742
Click here for the answer
Answer. 625
Explanation: The natural numbers ending with 2, 3, 7, and 8 do not form perfect squares. As a result, the number 625 is a perfect square. 625 is the square of 25.
Question 3. What is the value of 162-3?
Click here for the answer
Answer. 253
Explanation: The square of 16 is 256. 256-3 = 253
Question 4. Which of the following square will have 9 at the unit place?
- (33)2
- (25)2
- (86)2
- (94)2
Click here for the answer
Answer. (33)2
Explanation: The unit digit is 3 and the square of 3 is 9. Hence, (33)2 will have 9 at the unit place.
Question 5. What is the square root of 1764?
Click here for the answer
Answer. 42
Explanation: The square root of 1764= 42 x 42, Hence the square root is 42.
Question 6. What is the perfect square between 75 and 90?
Click here for the answer
Answer. 81
Explanation: 81 is the only perfect square that lies between75 and 90
Question 7. Solve 52 + (64)½
Click here for the answer
Answer. 33
Explanation: The square of 5 is 25 and the square root of 64 is 8. Hence, 25 + 8= 33
Question 8. Solve: 182 + 422
Click here for the answer
Answer. 2088
Explanation: The square of 18 is 324 and the square of 42 is 2088. Hence, 182 + 422 = 2088
Question 9. Which of the following do not have a perfect square root?
- 50
- 102
- 324
- 12
Click here for the answer
Answer. 324
Explanation: The square root of 324 is 18. Hence, only 324 has a perfect square root.
Question 10. How many zeros are there in the square of 100?
Click here for the answer
Answer. 4
Explanation: The square of 100= 100x100 i.e., 10000
Question 11. What is the greatest 3 digits number which is a perfect square?
Click here for the answer
Answer. 961
Explanation: The greatest 3-digit number which is a perfect square is 961, the square of 31.
Question 12. What will be the unit digit if we square 27?
Click here for the answer
Answer. 9
Explanation: The unit digit in the square of 27 will be 9 because the square of unit digit 7 is 49. Hence 9 will be at the unit place.
Question 13. Solve 172 - 112?
Click here for the answer
Answer. 168
Explanation: The square of 17 is 289 and the square of 11 is 121. So, 289 - 121 = 168.
Question 14. How many natural numbers lie between 72 and 82?
Click here for the answer
Answer. 14
Explanation: Natural numbers between n2 and (n+1)2 is equal to 2n. So,
n=7
2xn = 2 x 7
= 14
Question 15. What is the smallest 4 digits that is a perfect square?
Click here for the answer
Answer. 1024
Explanation: The smallest 4-digit number which is a perfect square is 1024, It is the square of 32.
Also Read:
Comments