Answer :
### Q2. Which of the following cannot be a perfect square: 841, 529, 198, 392, 216, 8640?
To determine which numbers from the list cannot be a perfect square, we will examine each number individually:
1. 841
- Taking the square root of 841, we get 29.
- Since 29 squared equals 841, 841 is a perfect square.
2. 529
- Taking the square root of 529, we get 23.
- Since 23 squared equals 529, 529 is a perfect square.
3. 198
- Taking the square root of 198, we get approximately 14.07.
- Since the square root is not an integer, 198 is not a perfect square.
4. 392
- Taking the square root of 392, we get approximately 19.80.
- Since the square root is not an integer, 392 is not a perfect square.
5. 216
- Taking the square root of 216, we get approximately 14.70.
- Since the square root is not an integer, 216 is not a perfect square.
6. 8640
- Taking the square root of 8640, we get approximately 92.94.
- Since the square root is not an integer, 8640 is not a perfect square.
Therefore, the numbers which cannot be perfect squares are:
- 198
- 392
- 216
- 8640
### Q3. A square board has an area of 144 sq units. How long is each side of the board?
To find the side length of a square when its area is given, we use the formula for the area of a square:
[tex]\[ \text{Area} = \text{side length}^2 \][/tex]
Given the area is 144 sq units, we solve for the side length by taking the square root of the area:
[tex]\[ \text{side length} = \sqrt{144} \][/tex]
Thus:
[tex]\[ \text{side length} = 12 \][/tex]
So, each side of the board is 12 units long.
To determine which numbers from the list cannot be a perfect square, we will examine each number individually:
1. 841
- Taking the square root of 841, we get 29.
- Since 29 squared equals 841, 841 is a perfect square.
2. 529
- Taking the square root of 529, we get 23.
- Since 23 squared equals 529, 529 is a perfect square.
3. 198
- Taking the square root of 198, we get approximately 14.07.
- Since the square root is not an integer, 198 is not a perfect square.
4. 392
- Taking the square root of 392, we get approximately 19.80.
- Since the square root is not an integer, 392 is not a perfect square.
5. 216
- Taking the square root of 216, we get approximately 14.70.
- Since the square root is not an integer, 216 is not a perfect square.
6. 8640
- Taking the square root of 8640, we get approximately 92.94.
- Since the square root is not an integer, 8640 is not a perfect square.
Therefore, the numbers which cannot be perfect squares are:
- 198
- 392
- 216
- 8640
### Q3. A square board has an area of 144 sq units. How long is each side of the board?
To find the side length of a square when its area is given, we use the formula for the area of a square:
[tex]\[ \text{Area} = \text{side length}^2 \][/tex]
Given the area is 144 sq units, we solve for the side length by taking the square root of the area:
[tex]\[ \text{side length} = \sqrt{144} \][/tex]
Thus:
[tex]\[ \text{side length} = 12 \][/tex]
So, each side of the board is 12 units long.
