Solve the Square Root Expression: Finding √(36x)

In order to simplify the given expression, apply the following two laws of exponents:

a. The definition of root as an exponent:

$\sqrt[n]{a}=a^{\frac{1}{n}}$

b. The law of exponents for an exponent applied to terms in parentheses:

$(a\cdot b)^n=a^n\cdot b^n$

Begin by converting the square root to an exponent using the law of exponents mentioned in a:

$\sqrt{36x}= \\ \downarrow\\ (36x)^{\frac{1}{2}}=$

Next, use the law of exponents mentioned in b and apply the exponent to each factor within the parentheses:

$(36x)^{\frac{1}{2}}= \\ 36^{\frac{1}{2}}\cdot x^{{\frac{1}{2}}}=\\ \sqrt{36}\sqrt{x}=\\ \boxed{6\sqrt{x}}$$$

In the final steps, we first converted the power of one-half applied to each factor in the multiplication back to square root form, again, according to the definition of root as an exponent mentioned in a (in the opposite direction) and then calculated the known square root of 36.

Therefore, the correct answer is answer c.