Multiply Square Roots: Solving √7 × √7

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 multiplication between terms with identical bases:

$a^m\cdot a^n=a^{m+n}$

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

$\sqrt{7}\cdot\sqrt{7}= \\ \downarrow\\ 7^{\frac{1}{2}}\cdot7^{\frac{1}{2}}=$We'll continue, since we are multiplying two terms with identical bases - we'll use the law of exponents mentioned in b:

$7^{\frac{1}{2}}\cdot7^{\frac{1}{2}}= \\ 7^{\frac{1}{2}+\frac{1}{2}}=\\ 7^1=\\ \boxed{7}$Therefore, the correct answer is answer a.