To determine which of the given squares ends with the digit 9, we need to find the last digit of the square for each number. This can be done by squaring each number and checking the units digit of the result.
Let's go through each option one by one:
1. For [tex]\( 607^2 \)[/tex]:
The units digit of 607 is 7. We need to find the units digit of [tex]\( 7^2 \)[/tex]. The square of 7 is:
[tex]\[
7^2 = 49
\][/tex]
The units digit of [tex]\( 607^2 \)[/tex] is 9.
2. For [tex]\( 609^2 \)[/tex]:
The units digit of 609 is 9. We need to find the units digit of [tex]\( 9^2 \)[/tex]. The square of 9 is:
[tex]\[
9^2 = 81
\][/tex]
The units digit of [tex]\( 609^2 \)[/tex] is 1.
3. For [tex]\( 605^2 \)[/tex]:
The units digit of 605 is 5. We need to find the units digit of [tex]\( 5^2 \)[/tex]. The square of 5 is:
[tex]\[
5^2 = 25
\][/tex]
The units digit of [tex]\( 605^2 \)[/tex] is 5.
4. For [tex]\( 604^2 \)[/tex]:
The units digit of 604 is 4. We need to find the units digit of [tex]\( 4^2 \)[/tex]. The square of 4 is:
[tex]\[
4^2 = 16
\][/tex]
The units digit of [tex]\( 604^2 \)[/tex] is 6.
Summarizing the results:
- The units digit of [tex]\( 607^2 \)[/tex] is 9
- The units digit of [tex]\( 609^2 \)[/tex] is 1
- The units digit of [tex]\( 605^2 \)[/tex] is 5
- The units digit of [tex]\( 604^2 \)[/tex] is 6
Only [tex]\( 607^2 \)[/tex] ends with the digit 9. Therefore, the correct answer is:
a) [tex]\( 607^2 \)[/tex]
