To determine which values satisfy the inequality [tex]\(\sqrt{x} \geq 25\)[/tex], we need to follow a systematic process. The key here is to find [tex]\(x\)[/tex] such that its square root is greater than or equal to 25. Let's go through each option step by step.
1. For [tex]\(x = 5\)[/tex]:
[tex]\[
\sqrt{5} \approx 2.236
\][/tex]
Since [tex]\(2.236 < 25\)[/tex], [tex]\(5\)[/tex] does not satisfy the inequality.
2. For [tex]\(x = 125\)[/tex]:
[tex]\[
\sqrt{125} \approx 11.180
\][/tex]
Since [tex]\(11.180 < 25\)[/tex], [tex]\(125\)[/tex] does not satisfy the inequality.
3. For [tex]\(x = 625\)[/tex]:
[tex]\[
\sqrt{625} = 25
\][/tex]
Since [tex]\(25 \geq 25\)[/tex], [tex]\(625\)[/tex] satisfies the inequality.
4. For [tex]\(x = -5\)[/tex]:
The square root of a negative number is not a real number. Therefore, [tex]\(-5\)[/tex] does not satisfy the inequality.
5. For [tex]\(x = -625\)[/tex]:
Similarly, the square root of a negative number is not a real number. Therefore, [tex]\(-625\)[/tex] does not satisfy the inequality.
6. For [tex]\(x = 700\)[/tex]:
[tex]\[
\sqrt{700} \approx 26.457
\][/tex]
Since [tex]\(26.457 \geq 25\)[/tex], [tex]\(700\)[/tex] satisfies the inequality.
In summary, the values that are solutions to the inequality [tex]\(\sqrt{x} \geq 25\)[/tex] are:
- C. 625
- F. 700
So, the correct answers are:
[tex]\[
\boxed{C, F}
\][/tex]
