What are the square roots of 100? Check all that apply.
A. 5
B. 10.5
C. -10
D. 10
E. -5
F. |10|
The Correct Answer and Explanation is:
The correct answers are:
C. -10
D. 10
F. |10|
Explanation:
To understand the square roots of 100, we first need to define what a square root is. The square root of a number ( x ) is a number ( y ) such that ( y^2 = x ). For 100, this means we are looking for numbers ( y ) such that ( y^2 = 100 ).
1. Positive Square Root:
The positive square root of 100 is straightforward. We know:
[ 10^2 = 100 ]
Therefore, one of the square roots of 100 is ( 10 ), which corresponds to option D.
2. Negative Square Root:
Square roots can also be negative because multiplying two negative numbers results in a positive number. For example:
[ (-10)^2 = 100 ]
Thus, the negative square root of 100 is ( -10 ), corresponding to option C.
3. Absolute Value:
The notation ( |10| ) refers to the absolute value of 10, which is always positive, regardless of the sign of the number inside the absolute value bars. In this case:
[ |10| = 10 ]
Since ( |10| ) equals 10, this also represents the positive square root of 100, corresponding to option F.
Why are the other options incorrect?
- A. 5: The square of 5 is ( 5^2 = 25 ), not 100.
- B. 10.5: The square of 10.5 is ( 10.5^2 = 110.25 ), which is not equal to 100.
- E. -5: The square of -5 is ( (-5)^2 = 25 ), not 100.
Therefore, the correct answers are C, D, and F. The square roots of 100 are 10 and -10, while ( |10| ) represents the positive root.