Solve x^2=81 using square roots. Explain or show your work.(1 point)

1 answer

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 \( x = -9 \).