simplify. $sqrt{32}$

Explanation:

Step1: Prime - factorize 32

$32 = 2\times2\times2\times2\times2$

Step2: Rewrite the square - root

$\sqrt{32}=\sqrt{2\times2\times2\times2\times2}$

Step3: Group the factors in pairs

$\sqrt{32}=\sqrt{(2\times2)\times(2\times2)\times2}$

Step4: Take the square - root of each pair

$\sqrt{(2\times2)\times(2\times2)\times2}=2\times2\sqrt{2}$

Step5: Calculate the product

$2\times2\sqrt{2}=4\sqrt{2}$

Answer:

$4\sqrt{2}$