find the roots of this equation by extracting the square roots with complete solution, k²=76

To find the roots of the equation \( k^2 = 76 \) by extracting the square roots, follow these steps:

### Step-by-Step Solution:

1. **Write down the equation:**
   \[ k^2 = 76 \]

2. **Take the square root of both sides of the equation:**
   \[ \sqrt{k^2} = \sqrt{76} \]

3. **Simplify the square root:**
   \[ k = \pm \sqrt{76} \]

4. **Simplify \(\sqrt{76}\) if possible:**
   \[ \sqrt{76} = \sqrt{4 \cdot 19} = \sqrt{4} \cdot \sqrt{19} = 2\sqrt{19} \]

5. **Write the final roots:**
   \[ k = \pm 2\sqrt{19} \]

### Conclusion:
The roots of the equation \( k^2 = 76 \) are \( k = 2\sqrt{19} \) and \( k = -2\sqrt{19} \).

Would you like further details or have any questions about this solution?

### Related Questions:
1. What is the general method for solving quadratic equations by extracting square roots?
2. How do you simplify expressions involving square roots?
3. Can you explain the significance of the plus-minus symbol (\(\pm\)) in root extraction?
4. How do you handle negative numbers under the square root?
5. What are the other methods to solve quadratic equations?
6. Can you provide examples of solving quadratic equations with complex numbers?
7. How do you verify the roots of a quadratic equation?
8. What is the quadratic formula and how is it used?

### Tip:
Always remember to consider both the positive and negative roots when solving equations involving square roots, as both values are solutions to the equation.

Learn how to find the roots of the equation k² = 76 by extracting square roots. This problem covers square root extraction and quadratic equations, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation