It looks like there are some typos and unclear parts in your question. Let's correct them for clarity:
1. "A perfect square number" might have the given digit?
(a) 3
(b) 4
(c) 7
(d) 8
2. A number has 5 zeroes at the end. Is it a perfect square or not?
3. [tex]\( (80)^2 \)[/tex] will have how many zeroes at the end?
4. [tex]\( (269)^2 \)[/tex] will be an odd or even number.
Now, let's address these questions step-by-step:
### 1. A perfect square number might have the given digit?
Perfect squares in the decimal system end with specific digits: 0, 1, 4, 5, 6, or 9. They do not end with the digits 2, 3, 7, or 8. Therefore, among the given options:
- (a) 3
- (b) 4
- (c) 7
- (d) 8
Only option (b) 4 can be the last digit of a perfect square.
Answer: (b) 4
### 2. A number has 5 zeroes at the end. Is it a perfect square or not?
For a number to be a perfect square and end with five zeros, it must be a multiple of [tex]\(10^5 = 100000\)[/tex]. So, the number would need to be a perfect square of [tex]\(100 \times n\)[/tex], where [tex]\(n\)[/tex] is an integer. However, in reality, for a number to end with an odd number of zeros and still be a perfect square, it must actually end with an even number of zeros.
For example, 10000 (which is [tex]\( 100^2\)[/tex]) ends with 4 zeros. So a perfect square that ends in exactly 5 zeros does not exist.
Answer: No, it is not a perfect square.
### 3. [tex]\((80)^2\)[/tex] will have how many zeroes at the end?
Calculate the square of 80.
[tex]\[ 80 \times 80 = 6400 \][/tex]
So, [tex]\( (80)^2 \)[/tex] = 6400 and the number 6400 has two zeros at the end.
Answer: 2 zeros.
### 4. [tex]\((269)^2\)[/tex] will be an odd or even number.
Check the parity of the square of 269.
Any integer squared retains the parity (odd/even characteristic) of the original number. Since 269 is an odd number:
[tex]\[ (odd)^2 = odd \][/tex]
So, [tex]\((269)^2\)[/tex] will be odd.
Answer: Odd.
I hope these explanations help clarify the questions and their answers! If you have any more questions or need further clarification, feel free to ask.
