Solve $\sqrt{72}$

Step-by-step solution

1. Step 1 · Extract the largest square factor
   $$72=36\cdot 2$$

   36 is the biggest perfect square dividing 72.

2. Step 2 · Product rule for radicals
   $$\sqrt{36}\sqrt{2}$$

   √(ab) = √a·√b for non-negative a and b.

3. Step 3 · Evaluate the perfect square
   $$6\sqrt{2}$$

   √36 = 6, and √2 stays irrational.