Multiply Square Roots: Solving √8 × √8

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.:

$\sqrt{8}\cdot\sqrt{8}= \\ \downarrow\\ 8^{\frac{1}{2}}\cdot8^{\frac{1}{2}}=$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 exponentiation on the term in parentheses:

$8^{\frac{1}{2}}\cdot8^{\frac{1}{2}}= \\ (8^{\frac{1}{2}})^2=\\ 8^{\frac{1}{2}\cdot2}=\\ 8^1=\\ \boxed{8}$Therefore, the correct answer is answer c.