Calculate √5 × √6: Multiplying Square Roots Step-by-Step

In order to simplify the given expression, apply 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 exponents applied to terms in parentheses (in reverse):

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

Begin by converting the square roots to exponents using the law of exponents mentioned in a':

$\sqrt{5}\cdot\sqrt{6}= \\ \downarrow\\ 5^{\frac{1}{2}}\cdot6^{\frac{1}{2}}=$

Due to the fact that there is multiplication between two terms with identical exponents, we are able to apply the law of exponents mentioned in b' and then proceed to combine them together inside of parentheses, raised to the same exponent:

$5^{\frac{1}{2}}\cdot6^{\frac{1}{2}}= \\ (5\cdot6)^{\frac{1}{2}}=\\ 30^{\frac{1}{2}}=\\ \boxed{\sqrt{30}}$

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) to return to root notation.

Therefore, the correct answer is answer d.