Find the solution(s) of the following equation.
\[b^2 = 49\]
Choose all answers that apply:
Choose all answers that apply:
(Choice A)   
\[b = 7\]
A
\[b = 7\]
(Choice B)   
\[b = -7\]
B
\[b = -7\]
(Choice C)   
\[b = \sqrt{49}\]
C
\[b = \sqrt{49}\]
(Choice D)   
\[b = -\sqrt{49}\]
D
\[b = -\sqrt{49}\]
(Choice E)   None of the above
E
None of the above

The given equation is:

\[
b^2 = 49
\]

To solve this, we need to find the values of \(b\) such that when squared, the result is 49. This can be done by taking the square root of both sides of the equation:

\[
b = \pm \sqrt{49}
\]

Since \(\sqrt{49} = 7\), the two solutions are:

\[
b = 7 \quad \text{and} \quad b = -7
\]

Now let's go through the choices:

- **Choice A**: \(b = 7\) is correct.
- **Choice B**: \(b = -7\) is also correct.
- **Choice C**: \(b = \sqrt{49}\), which simplifies to \(b = 7\), so this is correct.
- **Choice D**: \(b = -\sqrt{49}\), which simplifies to \(b = -7\), so this is also correct.
- **Choice E**: None of the above. This is incorrect since we have valid solutions.

Therefore, the correct answers are **Choices A, B, C, and D**.

Would you like further details or explanations?

---

Here are five related questions you might want to explore:

1. What is the general solution to the equation \(x^2 = c\) where \(c > 0\)?
2. How do we handle negative square roots in complex numbers?
3. What is the difference between \(\sqrt{x}\) and \(\pm \sqrt{x}\)?
4. How can we solve quadratic equations using square roots?
5. How do square roots relate to exponentiation?

**Tip**: Remember that taking the square root of a number yields both a positive and negative solution!

Find the solution(s) of the following equation. b^2 = 49. Choose all answers that apply:
(Choice A) b = 7
(Choice B) b = -7
(Choice C) b = \sqrt{49}
(Choice D) b = -\sqrt{49}
(Choice E) None of the above

Explore how to solve the equation b^2 = 49 by identifying all possible values of b. This problem involves key algebraic concepts like square roots and quadratic equations. It is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation