Use inspection to solve the equation x^2=10^10

Question

, selecting the correct solution set below. (1 point)
Responses

{−10^5,10^5}
left brace negative 10 superscript 5 baseline comma 10 superscript 5 baseline right brace

{−5^10,5^10}
left brace negative 5 superscript 10 baseline comma 5 superscript 10 baseline right brace

{10^5}

left brace 10 superscript 5 baseline right brace

{−5^5}

Answer 1

To solve the equation \( x^2 = 10^{10} \), we can take the square root of both sides. The square root operation yields both a positive and a negative solution.

Calculating the square root:

\[ x = \pm \sqrt{10^{10}} = \pm 10^{5} \]

Thus, the solutions are:

\[ x = 10^5 \quad \text{and} \quad x = -10^5 \]

This means the solution set is:

\[ { -10^5, 10^5 } \]

So, the correct response is:

\[ {−10^5, 10^5} \]