https://file.aiquickdraw.com/mathbot/file/17259870827221ttrv1is.jpg

To solve for \( y \) in the given equation:

\[
\sqrt{x + 2y} = z
\]

First, we square both sides to remove the square root:

\[
(\sqrt{x + 2y})^2 = z^2
\]

This simplifies to:

\[
x + 2y = z^2
\]

Next, we isolate \( y \) by subtracting \( x \) from both sides:

\[
2y = z^2 - x
\]

Finally, we divide by 2:

\[
y = \frac{z^2 - x}{2}
\]

So, the correct answer is:

\[
y = \frac{z^2 - x}{2}
\]

This matches the option in the bottom left of the provided answers.

Do you want more details or have any questions? Here are 5 related questions to expand your understanding:

1. How do you solve an equation involving a square root?
2. What are the steps to isolate a variable in an algebraic equation?
3. Can you explain the process of squaring both sides of an equation?
4. How do you verify if your solution to an equation is correct?
5. What other methods can be used to solve equations involving square roots?

**Tip:** When solving equations, always perform the same operation on both sides to maintain equality.

Solve for y in the following equation: \( \sqrt{x + 2y} = z \).

Learn how to solve for y in the equation √(x + 2y) = z. This step-by-step guide covers key algebraic concepts, including squaring both sides of an equation and isolating variables. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation