The equation \( x^2 - 27 = 0 \) can be solved by isolating \( x^2 \):

1. Add 27 to both sides:
   \[
   x^2 = 27
   \]

2. Take the square root of both sides:
   \[
   x = \pm \sqrt{27}
   \]

3. Simplify \( \sqrt{27} \):
   \[
   \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}
   \]

Thus, the solutions are:
\[
x = \pm 3\sqrt{3}
\]

Would you like further explanation or details?

Here are 5 related questions for further practice:
1. Solve \( x^2 - 16 = 0 \).
2. Solve \( x^2 - 45 = 0 \).
3. What are the solutions to \( x^2 - 50 = 0 \)?
4. Solve \( x^2 + 25 = 0 \) and explain how it differs.
5. How do you solve \( x^2 = 2 \)?

**Tip**: Always check if a square root can be simplified by factoring out perfect squares!

Learn how to solve the quadratic equation x² - 27 = 0 step-by-step. This solution covers the properties of square roots and simplifying radicals, making it suitable for students in Grades 8-10. Perfect for practicing algebraic skills.

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