To solve the equation:

$8 = \sqrt{2^x}$

First, rewrite the square root as an exponent:

$\sqrt{2^x} = (2^x)^{1/2}$

This gives us the equation:

$8 = (2^x)^{1/2}$

Now square both sides to eliminate the square root:

$8^2 = 2^x$

$64 = 2^x$

Now express 64 as a power of 2:

$64 = 2^6$

Therefore, we have:

$2^x = 2^6$

Since the bases are the same, the exponents must be equal:

$x = 6$

Thus, the solution is:

$x = 6$

Do you want more details or have any questions?

Here are some related questions:

1. How do you solve equations with fractional exponents?
2. What is the general method to solve exponential equations?
3. How does the property of exponents work when bases are equal?
4. How do you solve logarithmic equations?
5. What are the different ways to express roots using exponents?

Tip: When dealing with square roots, remember that $\sqrt{x} = x^{1/2}$.