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: \[ x = 100000 \quad \text{or} \quad x = -100000 \]