Multiply Square Roots: Calculate √10 × √2 × √5

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 a product in parentheses (in reverse direction):

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

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

$\sqrt{10}\cdot\sqrt{2}\cdot\sqrt{5} \\ \downarrow\\ 10^{\frac{1}{2}}\cdot2^{\frac{1}{2}}\cdot5^{\frac{1}{2}}=$

We'll continue, since there is a multiplication between three terms with identical exponents we can use the law of exponents mentioned in b (which also applies to multiplying several terms in parentheses) and combine them together in a multiplication under parentheses which are raised to the same exponent:

$10^{\frac{1}{2}}\cdot2^{\frac{1}{2}}\cdot5^{\frac{1}{2}}= \\ (10\cdot2\cdot5)^{\frac{1}{2}}=\\ 100^{\frac{1}{2}}=\\ \sqrt{100}=\\ \boxed{10}$

In the final steps, we first performed the multiplication within the parentheses, then we used again the definition of root as an exponent mentioned in a (in reverse direction) to return to root notation, and in the final stage we calculated the known square root of 100.

Therefore, we can identify that the correct answer (most appropriate) is answer d.