Answer :
Let’s solve each part of the problem step-by-step.
### Part 1: [tex]\( -\sqrt{9} \)[/tex]
1. Calculate the square root of 9:
[tex]\[ \sqrt{9} = 3 \][/tex]
2. Negate the result:
[tex]\[ -\sqrt{9} = -3 \][/tex]
So,
[tex]\[ -\sqrt{9} = -3 \][/tex]
### Part 2: [tex]\( \sqrt{-25} \)[/tex]
1. Recognize that the square root of a negative number involves complex numbers:
- The square root of [tex]\(-25\)[/tex] can be expressed using the imaginary unit [tex]\( i \)[/tex], where [tex]\( i = \sqrt{-1} \)[/tex].
2. Rewrite -25 as a product of -1 and a positive number:
[tex]\[ -25 = -1 \times 25 \][/tex]
3. Take the square root of each part separately:
[tex]\[ \sqrt{-25} = \sqrt{-1 \times 25} = \sqrt{-1} \times \sqrt{25} \][/tex]
4. Substitute the known values:
[tex]\[ \sqrt{-1} = i \quad \text{and} \quad \sqrt{25} = 5 \][/tex]
5. Combine the results:
[tex]\[ \sqrt{-25} = i \times 5 = 5i \][/tex]
So,
[tex]\[ \sqrt{-25} = 5i \][/tex]
### Final Answers
[tex]\[ -\sqrt{9} = -3 \][/tex]
[tex]\[ \sqrt{-25} = 5i \][/tex]
### Part 1: [tex]\( -\sqrt{9} \)[/tex]
1. Calculate the square root of 9:
[tex]\[ \sqrt{9} = 3 \][/tex]
2. Negate the result:
[tex]\[ -\sqrt{9} = -3 \][/tex]
So,
[tex]\[ -\sqrt{9} = -3 \][/tex]
### Part 2: [tex]\( \sqrt{-25} \)[/tex]
1. Recognize that the square root of a negative number involves complex numbers:
- The square root of [tex]\(-25\)[/tex] can be expressed using the imaginary unit [tex]\( i \)[/tex], where [tex]\( i = \sqrt{-1} \)[/tex].
2. Rewrite -25 as a product of -1 and a positive number:
[tex]\[ -25 = -1 \times 25 \][/tex]
3. Take the square root of each part separately:
[tex]\[ \sqrt{-25} = \sqrt{-1 \times 25} = \sqrt{-1} \times \sqrt{25} \][/tex]
4. Substitute the known values:
[tex]\[ \sqrt{-1} = i \quad \text{and} \quad \sqrt{25} = 5 \][/tex]
5. Combine the results:
[tex]\[ \sqrt{-25} = i \times 5 = 5i \][/tex]
So,
[tex]\[ \sqrt{-25} = 5i \][/tex]
### Final Answers
[tex]\[ -\sqrt{9} = -3 \][/tex]
[tex]\[ \sqrt{-25} = 5i \][/tex]
