Question

Use inspection to solve the equation acts to the second power equals 10 to the 10th power selecting the correct solution below

Answer 1

To solve the equation \( x^2 = 10^{10} \) by inspection, we can take the square root of both sides.

1. Start with the equation:
\[
x^2 = 10^{10}
\]

2. Taking the square root of both sides, we have:
\[
x = \sqrt{10^{10}}
\]

3. Using the property of square roots:
\[
\sqrt{a^2} = a \quad \text{and} \quad \sqrt{a^b} = a^{b/2}
\]
Applying this to our equation:
\[
x = 10^{10/2} = 10^5
\]

Thus, the solution is:
\[
x = 10^5 = 100000
\]

Also, remember that when we take the square root, we consider both the positive and negative solutions. So:

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

Therefore, the correct solutions are:
\[
x = 100000 \quad \text{or} \quad x = -100000
\]