To find the square roots of 100, we need to determine the numbers which, when squared, equal 100. Mathematically, these solutions are expressed as numbers [tex]\( x \)[/tex] such that [tex]\( x^2 = 100 \)[/tex].
Step-by-step solution:
1. Calculate the positive square root of 100:
The number that, when squared, equals 100 can be found by:
[tex]\[
\sqrt{100} = 10
\][/tex]
This is because:
[tex]\[
10^2 = 100
\][/tex]
2. Calculate the negative square root of 100:
Negative numbers also have square roots, as squaring a negative number results in a positive number:
[tex]\[
\sqrt{100} = -10
\][/tex]
This is because:
[tex]\[
(-10)^2 = 100
\][/tex]
3. Check each option provided to see if it matches one of these square roots:
- Option A: 10.5
[tex]\[
10.5^2 = 110.25 \neq 100
\][/tex]
So, 10.5 is not a square root of 100.
- Option B: -10
[tex]\[
(-10)^2 = 100
\][/tex]
So, -10 is a square root of 100.
- Option C: [tex]\(|10|\)[/tex]
[tex]\[
|10| = 10
\][/tex]
So, 10 is indeed a square root of 100.
- Option D: -5
[tex]\[
(-5)^2 = 25 \neq 100
\][/tex]
So, -5 is not a square root of 100.
- Option E: 10
[tex]\[
10^2 = 100
\][/tex]
So, 10 is a square root of 100.
- Option F: 5
[tex]\[
5^2 = 25 \neq 100
\][/tex]
So, 5 is not a square root of 100.
Thus, the correct answers are:
- Option B: -10
- Option C: [tex]\(|10|\)[/tex], which simplifies to 10
- Option E: 10
