Multiply Square Roots: Calculate √5 × √10 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 an exponent applied to terms in parentheses (in reverse direction):

$x^n\cdot y^n =(x\cdot y)^n$

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

$\sqrt{5}\cdot\sqrt{10}= \\ \downarrow\\ 5^{\frac{1}{2}}\cdot10^{\frac{1}{2}}=$

We'll continue, since there is multiplication between two terms with identical exponents, we can use the law of exponents mentioned in b' and combine them together in parentheses which are raised to the same exponent:

$5^{\frac{1}{2}}\cdot10^{\frac{1}{2}}= \\ (5\cdot10)^{\frac{1}{2}}=\\ 50^{\frac{1}{2}}=\\ \boxed{\sqrt{50}}$

In the final steps, we performed the multiplication within the parentheses and again used the definition of root as an exponent mentioned in a' (in reverse direction) to return to root notation.

Therefore, the correct answer is answer c.