(d) The radical expression $$ \sqrt{32} $$ simplifies to $$ \square \sqrt{2} $$.

Question

UpStudy AI · Accepted Answer

1. Express $$32$$ as the product of a perfect square and another factor:
   $$
   32 = 16 \times 2
   $$

2. Rewrite the square root:
   $$
   \sqrt{32} = \sqrt{16 \times 2}
   $$

3. Use the property of radicals $$\sqrt{ab} = \sqrt{a} \times \sqrt{b}$$:
   $$
   \sqrt{32} = \sqrt{16} \times \sqrt{2}
   $$

4. Since $$\sqrt{16} = 4$$, substitute:
   $$
   \sqrt{32} = 4\sqrt{2}
   $$

Thus, the simplified form is $$4\sqrt{2}$$.
$$ \sqrt{32} = 4\sqrt{2} $$

(d) The radical expression simplifies to .