Question

use the product rule to simplify the radical.
\sqrt{47}

\sqrt{47} = \square (type an exact answer in simplified form.)

Explanation:

Step1: Identify factors of 47

47 is a prime number, its only positive factors are 1 and 47.

Step2: Apply product rule for radicals

The product rule for radicals states $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ for non-negative $a,b$. Since there are no perfect square factors other than 1, we cannot simplify further.

Answer:

$\sqrt{47}$