Use inspection to solve the equation x2=36169, then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)

Question

Responses

{−613,613}
left brace negative Start Fraction 6 over 13 End Fraction comma Start Fraction 6 over 13 End Fraction right brace

{613}
left brace Start Fraction 6 over 13 End Fraction right brace

There are no real solutions.
There are no real solutions.

{−613}

Answer 1

To solve the equation \( x^2 = 36169 \) by inspection, we can find the square roots of 36169:

\[ x = \pm \sqrt{36169} \]

Calculating \( \sqrt{36169} \):

Since \( 36169 \) is a perfect square, we find:

\[ \sqrt{36169} = 601 \]

Thus, the solutions to the equation are:

\[ x = 601 \quad \text{and} \quad x = -601 \]

Therefore, the solution set is:

\[ { -601, 601 } \]

From the provided options, the correct solution set is:

{−613,613}