To solve the inequality [tex]\(\sqrt{x} < 10\)[/tex], we need to determine which values of [tex]\(x\)[/tex] satisfy this condition. Let's examine each option provided:
1. [tex]\(x = 9\)[/tex]:
- Calculate the square root of 9:
[tex]\[
\sqrt{9} = 3
\][/tex]
- Check if [tex]\(3 < 10\)[/tex]:
[tex]\[
3 < 10 \quad \text{(True)}
\][/tex]
- Hence, 9 is a solution.
2. [tex]\(x = 36\)[/tex]:
- Calculate the square root of 36:
[tex]\[
\sqrt{36} = 6
\][/tex]
- Check if [tex]\(6 < 10\)[/tex]:
[tex]\[
6 < 10 \quad \text{(True)}
\][/tex]
- Hence, 36 is a solution.
3. [tex]\(x = 105\)[/tex]:
- Calculate the square root of 105:
[tex]\[
\sqrt{105} \approx 10.25
\][/tex]
- Check if [tex]\(10.25 < 10\)[/tex]:
[tex]\[
10.25 < 10 \quad \text{(False)}
\][/tex]
- Hence, 105 is not a solution.
4. [tex]\(x = 25\)[/tex]:
- Calculate the square root of 25:
[tex]\[
\sqrt{25} = 5
\][/tex]
- Check if [tex]\(5 < 10\)[/tex]:
[tex]\[
5 < 10 \quad \text{(True)}
\][/tex]
- Hence, 25 is a solution.
5. [tex]\(x = -100\)[/tex]:
- The square root of a negative number is not a real number, so:
[tex]\[
\sqrt{-100} \quad \text{(Not Defined in the Real Number System)}
\][/tex]
- Hence, -100 is not a solution.
6. [tex]\(x = 100\)[/tex]:
- Calculate the square root of 100:
[tex]\[
\sqrt{100} = 10
\][/tex]
- Check if [tex]\(10 < 10\)[/tex]:
[tex]\[
10 < 10 \quad \text{(False)}
\][/tex]
- Hence, 100 is not a solution.
The values that satisfy the inequality [tex]\(\sqrt{x} < 10\)[/tex] are:
- 9
- 36
- 25
Therefore, the correct answers are:
A. 9
B. 36
D. 25
