Find The Solution(s) Of The Following Equation: B 2 = 16 121 B^2 = \frac{16}{121} B 2 = 121 16 ​ Choose All Answers That Apply:A. B = 2 7 B = \frac{2}{7} B = 7 2 ​ B. B = − 2 7 B = -\frac{2}{7} B = − 7 2 ​ C. B = 4 11 B = \frac{4}{11} B = 11 4 ​ D. B = − 4 11 B = -\frac{4}{11} B = − 11 4 ​ E. None Of The Above

Solving the Equation: Uncovering the Solutions to $b^2 = \frac{16}{121}$

In mathematics, solving equations is a fundamental concept that helps us understand the relationships between variables. When we encounter an equation like $b^2 = \frac{16}{121}$, our goal is to find the value(s) of $b$ that satisfy this equation. In this article, we will delve into the world of quadratic equations and explore the solutions to this particular equation.

The given equation is $b^2 = \frac{16}{121}$. To solve for $b$, we need to isolate the variable $b$ by taking the square root of both sides of the equation. This is a fundamental concept in algebra, and it allows us to find the solutions to quadratic equations.

When we take the square root of both sides of the equation, we get:

$$\sqrt{b^2} = \sqrt{\frac{16}{121}}$$

Using the property of square roots, we can rewrite this as:

$$b = \pm \sqrt{\frac{16}{121}}$$

To simplify the square root, we can break down the fraction $\frac{16}{121}$ into its prime factors:

$$\frac{16}{121} = \frac{2^4}{11^2}$$

Now, we can take the square root of the numerator and the denominator separately:

$$\sqrt{\frac{2^4}{11^2}} = \frac{\sqrt{2^4}}{\sqrt{11^2}}$$

Using the property of square roots, we can rewrite this as:

$$\frac{2^2}{11} = \frac{4}{11}$$

Now that we have simplified the square root, we can find the solutions to the equation:

$$b = \pm \frac{4}{11}$$

This means that the solutions to the equation are $b = \frac{4}{11}$ and $b = -\frac{4}{11}$.

In conclusion, we have solved the equation $b^2 = \frac{16}{121}$ and found the solutions to be $b = \frac{4}{11}$ and $b = -\frac{4}{11}$. These solutions satisfy the equation, and they are the values of $b$ that make the equation true.

Based on our solution, we can conclude that the correct answers are:

• C. $b = \frac{4}{11}$
• D. $b = -\frac{4}{11}$

The other options, A and B, are not correct solutions to the equation.

Solving equations is an essential skill in mathematics, and it requires a deep understanding of algebraic concepts. By following the steps outlined in this article, we can solve quadratic equations and find the solutions that satisfy the equation. Whether you are a student or a professional, mastering the art of solving equations is crucial for success in mathematics and other fields.
Solving the Equation: Uncovering the Solutions to $b^2 = \frac{16}{121}$

Q: What is the first step in solving the equation $b^2 = \frac{16}{121}$?

A: The first step in solving the equation is to take the square root of both sides of the equation. This allows us to isolate the variable $b$ and find the solutions to the equation.

Q: Why do we need to take the square root of both sides of the equation?

A: Taking the square root of both sides of the equation is necessary because the equation is in the form of $b^2 = \frac{16}{121}$. By taking the square root, we can find the value of $b$ that satisfies the equation.

Q: How do we simplify the square root of $\frac{16}{121}$?

A: To simplify the square root of $\frac{16}{121}$, we can break down the fraction into its prime factors. This allows us to rewrite the fraction as $\frac{2^4}{11^2}$, which can then be simplified further.

Q: What is the simplified form of the square root of $\frac{16}{121}$?

A: The simplified form of the square root of $\frac{16}{121}$ is $\frac{4}{11}$.

Q: What are the solutions to the equation $b^2 = \frac{16}{121}$?

A: The solutions to the equation $b^2 = \frac{16}{121}$ are $b = \frac{4}{11}$ and $b = -\frac{4}{11}$.

Q: Why are there two solutions to the equation?

A: There are two solutions to the equation because the square root of a number can be positive or negative. In this case, the square root of $\frac{16}{121}$ is $\frac{4}{11}$, but it can also be $-\frac{4}{11}$.

Q: How do we know which solution is correct?

A: To determine which solution is correct, we need to plug the solution back into the original equation and check if it is true. In this case, both solutions satisfy the equation, so both are correct.

Q: What is the final answer to the equation $b^2 = \frac{16}{121}$?

A: The final answer to the equation $b^2 = \frac{16}{121}$ is $b = \frac{4}{11}$ and $b = -\frac{4}{11}$.

Q: Can we use this method to solve other quadratic equations?

A: Yes, we can use this method to solve other quadratic equations. The steps outlined in this article can be applied to any quadratic equation in the form of $b^2 = c$, where $c$ is a constant.

Q: What are some common mistakes to avoid when solving quadratic equations?

A: Some common mistakes to avoid when solving quadratic equations include:

• Not taking the square root of both sides of the equation
• Not simplifying the square root
• Not checking if the solution satisfies the original equation
• Not considering both positive and negative solutions

By avoiding these common mistakes, you can ensure that you are solving quadratic equations correctly and accurately.