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Answer :
To solve the equation [tex]\( n^2 = 100 \)[/tex], we need to find the values of [tex]\( n \)[/tex] that satisfy this equation. Here are the steps for solving this equation:
1. Understand the equation: The equation given is [tex]\( n^2 = 100 \)[/tex]. This means we are looking for the numbers [tex]\( n \)[/tex] such that when [tex]\( n \)[/tex] is squared (multiplied by itself), it equals 100.
2. Solving for [tex]\( n \)[/tex]:
- To find [tex]\( n \)[/tex], we need to take the square root of both sides of the equation. Taking the square root of [tex]\( n^2 \)[/tex] gives us [tex]\( n \)[/tex], and taking the square root of 100 gives us both the positive and negative roots.
3. Calculate the square root:
[tex]\[ \sqrt{n^2} = \pm \sqrt{100} \][/tex]
- The square root of [tex]\( n^2 \)[/tex] is [tex]\( n \)[/tex], and the square root of 100 is 10. Therefore, we have:
[tex]\[ n = \pm 10 \][/tex]
- This means [tex]\( n \)[/tex] can be either 10 or -10 because both 10 squared and -10 squared equal 100.
4. Identify the solutions: The solutions to the equation [tex]\( n^2 = 100 \)[/tex] are therefore:
- [tex]\( n = 10 \)[/tex]
- [tex]\( n = -10 \)[/tex]
5. Choose the correct answers from the given options:
- We now look at the options provided:
- [tex]$-25$[/tex]
- [tex]$-10$[/tex]
- 10
- 25
- 50
6. Match the solutions:
- From our calculation, the solutions are 10 and -10.
- Comparing these with the options provided, the numbers -10 and 10 are the solutions.
Therefore, the two correct answers are:
- [tex]$-10$[/tex]
- 10
1. Understand the equation: The equation given is [tex]\( n^2 = 100 \)[/tex]. This means we are looking for the numbers [tex]\( n \)[/tex] such that when [tex]\( n \)[/tex] is squared (multiplied by itself), it equals 100.
2. Solving for [tex]\( n \)[/tex]:
- To find [tex]\( n \)[/tex], we need to take the square root of both sides of the equation. Taking the square root of [tex]\( n^2 \)[/tex] gives us [tex]\( n \)[/tex], and taking the square root of 100 gives us both the positive and negative roots.
3. Calculate the square root:
[tex]\[ \sqrt{n^2} = \pm \sqrt{100} \][/tex]
- The square root of [tex]\( n^2 \)[/tex] is [tex]\( n \)[/tex], and the square root of 100 is 10. Therefore, we have:
[tex]\[ n = \pm 10 \][/tex]
- This means [tex]\( n \)[/tex] can be either 10 or -10 because both 10 squared and -10 squared equal 100.
4. Identify the solutions: The solutions to the equation [tex]\( n^2 = 100 \)[/tex] are therefore:
- [tex]\( n = 10 \)[/tex]
- [tex]\( n = -10 \)[/tex]
5. Choose the correct answers from the given options:
- We now look at the options provided:
- [tex]$-25$[/tex]
- [tex]$-10$[/tex]
- 10
- 25
- 50
6. Match the solutions:
- From our calculation, the solutions are 10 and -10.
- Comparing these with the options provided, the numbers -10 and 10 are the solutions.
Therefore, the two correct answers are:
- [tex]$-10$[/tex]
- 10
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