What are the solutions to the equation $$ \sqrt{x+5=7} $$

The equation given is:

\[
\sqrt{x + 5} = 7
\]

To solve this equation, we need to eliminate the square root by squaring both sides:

\[
(\sqrt{x + 5})^2 = 7^2
\]

This simplifies to:

\[
x + 5 = 49
\]

Next, we solve for $ x $ by subtracting 5 from both sides:

\[
x = 49 - 5
\]

\[
x = 44
\]

So, the solution is $ x = 44 $.

Do you want more details on the solving process or have any questions?

Here are five related questions to expand on this concept:

1. How do you solve equations involving cube roots?
2. What is the general method for solving equations with exponents?
3. How would you solve $ \sqrt{2x + 3} = 5 $?
4. What happens if the square root is on both sides of the equation?
5. How do you verify that your solution to a square root equation is correct?

**Tip:** Always check your solution in the original equation, especially when dealing with square roots, to ensure it's valid and doesn't introduce extraneous solutions.

Learn how to solve the equation sqrt(x + 5) = 7 with detailed steps. This problem covers square roots, equations, and squaring both sides method. Suitable for Grades 7-9 students.

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