Express in simplest radical form. Answer Attemptiout of square sqrt (32)

To simplify the square root of 32, we need to find the prime factorization of 32 and then identify pairs of prime factors.<br /><br />The prime factorization of 32 is:<br />\[ 32 = 2 \times 16 = 2 \times 2 \times 8 = 2 \times 2 \times 2 \times 4 = 2 \times 2 \times 2 \times 2 \times 2 \]<br /><br />So, the prime factorization of 32 is:<br />\[ 32 = 2^5 \]<br /><br />Next, we can rewrite the square root of 32 using its prime factorization:<br />\[ \sqrt{32} = \sqrt{2^5} \]<br /><br />We can simplify this by recognizing that:<br />\[ \sqrt{2^5} = \sqrt{2^4 \times 2} = \sqrt{(2^2)^2 \times 2} = \sqrt{4^2 \times 2} = 4\sqrt{2} \]<br /><br />Therefore, the simplest radical form of \(\sqrt{32}\) is:<br />\[ \boxed{4\sqrt{2}} \]