Multiply Square Roots: Calculate √3 × √3

In order to simplify the given expression, we will use two laws of exponents:

a. The definition of a 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:

$\sqrt{3}\cdot\sqrt{3}= \\ \downarrow\\ 3^{\frac{1}{2}}\cdot3^{\frac{1}{2}}=$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 of the term in parentheses:

$3^{\frac{1}{2}}\cdot3^{\frac{1}{2}}= \\ (3^{\frac{1}{2}})^2=\\ 3^{\frac{1}{2}\cdot2}=\\ 3^1=\\ \boxed{3}$Additionally, we identify that:

$3=\sqrt{9}$Therefore, the correct answer (most accurate) is answer d.