Sure, let's go through each problem step-by-step:
### Problem 31: [tex]\(\sqrt{25}\)[/tex]
To find the square root of 25, we need to determine the number that, when multiplied by itself, gives 25.
- [tex]\(\sqrt{25} = 5\)[/tex]
Hence, the square root of 25 is [tex]\(5.0\)[/tex].
### Problem 32: [tex]\(-\sqrt{81}\)[/tex]
To find the negative square root of 81, we need to determine the number that, when multiplied by itself, gives 81, and then take the negative of that number.
- The positive square root of 81 is [tex]\(9\)[/tex].
- Therefore, [tex]\(-\sqrt{81} = -9\)[/tex]
Hence, the negative square root of 81 is [tex]\(-9.0\)[/tex].
### Problem 33: [tex]\(\pm \sqrt{9}\)[/tex]
The symbol ± indicates that we need both the positive and negative square roots of 9.
- The positive square root of 9 is [tex]\(3\)[/tex].
- The negative square root of 9 is [tex]\(-3\)[/tex].
Hence, [tex]\(\pm \sqrt{9}\)[/tex] is [tex]\(3.0\)[/tex] and [tex]\(-3.0\)[/tex].
### Problem 34: [tex]\(-\sqrt{144}\)[/tex]
To find the negative square root of 144, we need to determine the number that, when multiplied by itself, gives 144, and then take the negative of that number.
- The positive square root of 144 is [tex]\(12\)[/tex].
- Therefore, [tex]\(-\sqrt{144} = -12\)[/tex]
Hence, the negative square root of 144 is [tex]\(-12.0\)[/tex].
So, compiling all the results, we have:
- [tex]\(\sqrt{25} = 5.0\)[/tex]
- [tex]\(-\sqrt{81} = -9.0\)[/tex]
- [tex]\(\pm \sqrt{9} = (3.0, -3.0)\)[/tex]
- [tex]\(-\sqrt{144} = -12.0\)[/tex]
