At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.