Question
Solve x^2=81 using square roots. Explain or show your work.(1 point)
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 = 81 \) using square roots, follow these steps:
1. **Identify the equation**: We have \( x^2 = 81 \).
2. **Take the square root of both sides**: When we take the square root of both sides, we need to remember that there are both positive and negative roots. Thus, we write:
\[
x = \pm \sqrt{81}
\]
3. **Calculate the square root**: The square root of 81 is 9. Therefore:
\[
x = \pm 9
\]
4. **Write the final answers**: This gives us two solutions:
\[
x = 9 \quad \text{and} \quad x = -9
\]
In summary, the solutions to the equation \( x^2 = 81 \) are \( x = 9 \) and \( x = -9 \).
1. **Identify the equation**: We have \( x^2 = 81 \).
2. **Take the square root of both sides**: When we take the square root of both sides, we need to remember that there are both positive and negative roots. Thus, we write:
\[
x = \pm \sqrt{81}
\]
3. **Calculate the square root**: The square root of 81 is 9. Therefore:
\[
x = \pm 9
\]
4. **Write the final answers**: This gives us two solutions:
\[
x = 9 \quad \text{and} \quad x = -9
\]
In summary, the solutions to the equation \( x^2 = 81 \) are \( x = 9 \) and \( x = -9 \).