To solve the equation:

\[
r^2 - 24 = 0
\]

1. Add \( 24 \) to both sides to isolate the term with \( r \):
   \[
   r^2 = 24
   \]

2. Take the square root of both sides:
   \[
   r = \pm \sqrt{24}
   \]

3. Simplify \( \sqrt{24} \) by breaking it down into prime factors:
   \[
   \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}
   \]

Thus, the solutions are:
\[
r = \pm 2\sqrt{6}
\]

Would you like further details on any of these steps, or have any questions?

---

Here are five related questions that could help expand understanding:

1. How do we handle square root simplification in other cases?
2. What happens if the equation has an additional term, such as \( r^2 - 24 + 5 = 0 \)?
3. How does the solution change if the equation is \( r^3 - 24 = 0 \)?
4. What if we had \( r^2 = -24 \) in this equation? How would imaginary numbers come into play?
5. How would the solution differ if we had \( r^4 - 24 = 0 \) instead?

**Tip:** Remember that square roots are simplified by factoring out perfect squares, such as \( 4, 9, 16, \) etc.

Learn how to solve the equation r^2 - 24 = 0 by isolating r and simplifying square roots. This guide walks through step-by-step, making it accessible for Grades 8-10 students who are studying square root properties in algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation