**Extract the Roots:** Solve (x-5)^2=36 by extracting the roots, and identify the roots. 

To solve the equation \( (x - 5)^2 = 36 \) by extracting the roots, follow these steps:

1. **Take the square root of both sides**: To eliminate the square, take the square root of both sides of the equation.
   \[
   \sqrt{(x - 5)^2} = \pm\sqrt{36}
   \]

2. **Simplify**: The square root of \( (x - 5)^2 \) is \( x - 5 \), and the square root of \( 36 \) is \( 6 \). Don't forget the \( \pm \) sign since there are both positive and negative roots.
   \[
   x - 5 = \pm 6
   \]

3. **Solve for \(x\)**: This gives two possible equations:
   \[
   x - 5 = 6 \quad \text{or} \quad x - 5 = -6
   \]

   Solving each:
   - For \( x - 5 = 6 \):
     \[
     x = 6 + 5 = 11
     \]
   - For \( x - 5 = -6 \):
     \[
     x = -6 + 5 = -1
     \]

4. **Identify the roots**: The solutions (roots) are \( x = 11 \) and \( x = -1 \).

So, the roots of the equation \( (x - 5)^2 = 36 \) are \( x = 11 \) and \( x = -1 \).

Would you like more details or have any questions?

---

Here are 5 related questions:
1. How do you solve quadratic equations by completing the square?
2. What is the significance of the discriminant in a quadratic equation?
3. How do you solve equations that involve absolute values?
4. Can every quadratic equation be solved by extracting the square root?
5. What is the geometric interpretation of the roots of a quadratic equation?

**Tip:** When taking the square root of both sides of an equation, always remember to consider both the positive and negative roots (i.e., \( \pm \)).

Learn how to extract roots from the equation (x-5)^2=36 step-by-step. Understand the quadratic formula and how to apply it to solve quadratic equations effectively. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation