Answer:
Step-by-step explanation:
[tex]\frac{\sqrt{32} }{\sqrt{16} - \sqrt{2} } = \frac{4\sqrt{2} }{4 - \sqrt{2} } ----------------- (1)[/tex]
It says it can be written in the form of
[tex]\frac{A\sqrt{B} + C }{D}[/tex]
where A, B, C and D are integers, D is positive and B is not divisible by square of any prime
Rationalize equation 1:
[tex]\frac{4\sqrt{2} }{4 - \sqrt{2} } X \frac{4 + \sqrt{2} }{4 + \sqrt{2}}[/tex]
in denominator, use (a + b)(a - b) = [tex]a^{2} - b^{2}[/tex]
After multiplying numerator and denominator you should get
[tex]\frac{16\sqrt{2} + 8}{14}[/tex]
this is in the form
[tex]\frac{A\sqrt{B} + C }{D}[/tex]
where A = 16, B = 2, C = 8, and D = 14
hope this helps you ^^
