The equation given is:

\[
x = \sqrt{3 + y}
\]

To work with this equation, we can isolate \( y \) by squaring both sides. Here's the step-by-step solution:

1. **Square both sides** to eliminate the square root:

\[
x^2 = (\sqrt{3 + y})^2
\]

which simplifies to:

\[
x^2 = 3 + y
\]

2. **Solve for \( y \)**:

\[
y = x^2 - 3
\]

So, the equation solved for \( y \) is:

\[
\boxed{y = x^2 - 3}
\]

### Key Points:
- \( x = \sqrt{3 + y} \) represents a relationship where \( x \) is the square root of an expression involving \( y \).
- After squaring both sides, the equation becomes quadratic in form, allowing us to isolate \( y \).

Would you like more details or have any questions about the solution?

### Related Questions:
1. What is the domain of the function \( x = \sqrt{3 + y} \)?
2. What is the range of the function \( y = x^2 - 3 \)?
3. How does the graph of \( y = x^2 - 3 \) look, and how is it related to \( x = \sqrt{3 + y} \)?
4. What happens if we add a constant to the square root, like \( x = \sqrt{3 + y} + 2 \)?
5. Can we express \( y \) in terms of \( x \) for other radical equations, such as \( x = \sqrt{2y + 5} \)?

### Tip:
When solving equations involving square roots, always remember to check for extraneous solutions that can arise from squaring both sides of the equation.

Explore the step-by-step process to solve the radical equation x = √(3 + y) for y. Understand key algebraic concepts, including radical equations and the properties of square roots, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation