Solve x^2=7^8 by inspection. There are two real solutions. Enter the lesser number first, and use exponents in your responses.

Answer 1

By inspection, we can observe that the base of both sides of the equation is 7. Therefore, we can equate their exponents:

⟹ x^2 = 7^8

Since both sides of the equation have the same base, the exponents must also be equal:

⟹ x^2 = 8

Taking the square root of both sides, we find:

⟹ x = ±√8

Simplifying the square root of 8, we have:

⟹ x = ±√(4 × 2)
⟹ x = ±√4 × √2
⟹ x = ±2 × √2

The two real solutions are ±2√2.

Since we are asked to enter the lesser solution first, the correct response is:

x = -2√2, 2√2.