Question

Solve the radical equation:

x−6−−−−√+2=3
(1 point)
Responses

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7
7

3
3

6

Answer 1

To solve the equation \( \sqrt{x - 6} + 2 = 3 \), we can follow these steps:

1. Isolate the radical on one side of the equation:

\[
\sqrt{x - 6} = 3 - 2
\]

This simplifies to:

\[
\sqrt{x - 6} = 1
\]

2. Square both sides to eliminate the square root:

\[
(\sqrt{x - 6})^2 = 1^2
\]

This gives:

\[
x - 6 = 1
\]

3. Solve for \( x \):

\[
x = 1 + 6
\]

Thus:

\[
x = 7
\]

4. Check the solution by substituting \( x = 7 \) back into the original equation:

\[
\sqrt{7 - 6} + 2 = 3
\]

This simplifies to:

\[
\sqrt{1} + 2 = 3
\]

Which is:

\[
1 + 2 = 3
\]

Since this statement is true, the solution is valid.

Therefore, the final answer is:

\[
\boxed{7}
\]