Answer :
To solve the inequality [tex]\(\sqrt{x} \geq 9\)[/tex], we need to consider what it means and then identify the values from the list that satisfy this inequality.
### Steps to Solve the Inequality:
1. Understanding the Inequality: The inequality [tex]\(\sqrt{x} \geq 9\)[/tex] implies that the square root of [tex]\(x\)[/tex] is greater than or equal to 9.
2. Removing the Square Root: To remove the square root, we square both sides of the inequality. This gives:
[tex]\[
x \geq 9^2
\][/tex]
3. Calculating the Square: Calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
Therefore, [tex]\(x \geq 81\)[/tex].
4. Considering Domain: The function [tex]\(\sqrt{x}\)[/tex] is only defined for [tex]\(x \geq 0\)[/tex]. Thus, we only consider non-negative values for [tex]\(x\)[/tex].
5. Checking Each Value: Now we need to check each given number from the problem to see which ones satisfy [tex]\(x \geq 81\)[/tex] and [tex]\(x \geq 0\)[/tex].
- 81: [tex]\(\sqrt{81} = 9\)[/tex]. 81 satisfies [tex]\(\sqrt{x} \geq 9\)[/tex].
- 27: [tex]\(\sqrt{27} \approx 5.2\)[/tex], which is less than 9, so 27 does not satisfy the inequality.
- 3: [tex]\(\sqrt{3} \approx 1.7\)[/tex], which is less than 9, so 3 does not satisfy the inequality.
- -3: Since this is a negative number, [tex]\(\sqrt{-3}\)[/tex] is not a real number. It does not satisfy the inequality.
- 100: [tex]\(\sqrt{100} = 10\)[/tex], which is greater than 9. Therefore, 100 satisfies the inequality.
- -81: This is also negative and [tex]\(\sqrt{-81}\)[/tex] is not a real number, so it does not satisfy the inequality.
### Conclusion:
The solutions to the inequality [tex]\(\sqrt{x} \geq 9\)[/tex] from the given set of values are:
- 81
- 100
### Steps to Solve the Inequality:
1. Understanding the Inequality: The inequality [tex]\(\sqrt{x} \geq 9\)[/tex] implies that the square root of [tex]\(x\)[/tex] is greater than or equal to 9.
2. Removing the Square Root: To remove the square root, we square both sides of the inequality. This gives:
[tex]\[
x \geq 9^2
\][/tex]
3. Calculating the Square: Calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
Therefore, [tex]\(x \geq 81\)[/tex].
4. Considering Domain: The function [tex]\(\sqrt{x}\)[/tex] is only defined for [tex]\(x \geq 0\)[/tex]. Thus, we only consider non-negative values for [tex]\(x\)[/tex].
5. Checking Each Value: Now we need to check each given number from the problem to see which ones satisfy [tex]\(x \geq 81\)[/tex] and [tex]\(x \geq 0\)[/tex].
- 81: [tex]\(\sqrt{81} = 9\)[/tex]. 81 satisfies [tex]\(\sqrt{x} \geq 9\)[/tex].
- 27: [tex]\(\sqrt{27} \approx 5.2\)[/tex], which is less than 9, so 27 does not satisfy the inequality.
- 3: [tex]\(\sqrt{3} \approx 1.7\)[/tex], which is less than 9, so 3 does not satisfy the inequality.
- -3: Since this is a negative number, [tex]\(\sqrt{-3}\)[/tex] is not a real number. It does not satisfy the inequality.
- 100: [tex]\(\sqrt{100} = 10\)[/tex], which is greater than 9. Therefore, 100 satisfies the inequality.
- -81: This is also negative and [tex]\(\sqrt{-81}\)[/tex] is not a real number, so it does not satisfy the inequality.
### Conclusion:
The solutions to the inequality [tex]\(\sqrt{x} \geq 9\)[/tex] from the given set of values are:
- 81
- 100
