Solve x2=78

Question

by inspection. There are two real solutions. Enter the lesser number first and use exponents in your responses.

Answer 1

To solve the equation \( x^2 = 78 \) by inspection, we can take the square root of both sides.

The solutions are:

\[ x = \sqrt{78} \quad \text{and} \quad x = -\sqrt{78} \]

Now, to express these solutions using exponents:

The lesser number is: \[ -\sqrt{78} = -78^{1/2} \]

The greater number is: \[ \sqrt{78} = 78^{1/2} \]

Thus, the two solutions, written with the lesser first, are: \[ -78^{1/2} \quad \text{and} \quad 78^{1/2} \]