Solve the Square Root Product: √4 × √4 Step-by-Step

In order to simplify the given expression, we will use 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 power of a power:

$(a^m)^n=a^{m\cdot n}$

Let's start by converting the square roots to exponents using the law mentioned in a':

$\sqrt{4}\cdot\sqrt{4}= \\ \downarrow\\ 4^{\frac{1}{2}}\cdot4^{\frac{1}{2}}=$Let's continue, notice that we got a number multiplied by itself, therefore, according to the definition of exponents we can write the expression we got as a power of that same number, then - we'll use the law of exponents mentioned in b' and perform the exponent operation on the term in parentheses:

$4^{\frac{1}{2}}\cdot4^{\frac{1}{2}}= \\ (4^{\frac{1}{2}})^2=\\ 4^{\frac{1}{2}\cdot2}=\\ 4^1=\\ \boxed{4}$Therefore, the correct answer is answer c.