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Solve the radical equation:

x−6−−−−√+2=3
(1 point)
Responses

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7
7

3
3

6

1 answer

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:

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

  1. Square both sides to eliminate the square root:

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

This gives:

\[ x - 6 = 1 \]

  1. Solve for \( x \):

\[ x = 1 + 6 \]

Thus:

\[ x = 7 \]

  1. 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:

\[ \boxed{7} \]