To determine which of the following numbers has a specific unit place when squared, we need to calculate the unit place of the square of each number.
1. Calculating the units place of [tex]\( 19^2 \)[/tex]:
- [tex]\( 19^2 = 361 \)[/tex]
- The unit place of [tex]\( 361 \)[/tex] is [tex]\( 1 \)[/tex].
2. Calculating the units place of [tex]\( 27^2 \)[/tex]:
- [tex]\( 27^2 = 729 \)[/tex]
- The unit place of [tex]\( 729 \)[/tex] is [tex]\( 9 \)[/tex].
3. Calculating the units place of [tex]\( 24^2 \)[/tex]:
- [tex]\( 24^2 = 576 \)[/tex]
- The unit place of [tex]\( 576 \)[/tex] is [tex]\( 6 \)[/tex].
4. Calculating the units place of [tex]\( 855^2 \)[/tex]:
- To find the unit place, we only need to consider the unit place of [tex]\( 855 \)[/tex], which is [tex]\( 5 \)[/tex].
- Squaring this digit: [tex]\( 5^2 = 25 \)[/tex]
- The unit place of [tex]\( 25 \)[/tex] is [tex]\( 5 \)[/tex].
Given this information, the units places are as follows:
- [tex]\( 19^2 \)[/tex] has a unit place of [tex]\( 1 \)[/tex].
- [tex]\( 27^2 \)[/tex] has a unit place of [tex]\( 9 \)[/tex].
- [tex]\( 24^2 \)[/tex] has a unit place of [tex]\( 6 \)[/tex].
- [tex]\( 855^2 \)[/tex] has a unit place of [tex]\( 5 \)[/tex].
Thus, the only one with units place of [tex]\( 1 \)[/tex] is [tex]\( 19^2 \)[/tex].
Therefore, [tex]\( 19^2 \)[/tex] is the answer.
