Answer:
a = 25
b= 1
[tex]25(1 + \sqrt{2} )[/tex]
-Expand the brackets first
-than rationalise , to remove the square root from the denominator.
-lastly, simplify.
Hope I was able to help:)))
[tex] \boxed{25}( \boxed{1} + \sqrt{2} )[/tex]
Step-by-step explanation:
[tex] \frac{ {( \sqrt{32} + \sqrt{2} })^{2} }{ \sqrt{8} - 2} \\ \\ = \frac{ {( 4\sqrt{2} + \sqrt{2} })^{2} }{2 \sqrt{2} - 2} \\ \\ = \frac{ { {( \sqrt{2} )}^{2} ( 4 + 1 })^{2} }{2 (\sqrt{2} - 1)} \\ \\ = \frac{ { {2 ( 5} })^{2} }{2 (\sqrt{2} - 1)} \\ \\ = \frac{ 25 }{ (\sqrt{2} - 1)} \\ \\ = \frac{ 25( \sqrt{2} + 1) }{ (\sqrt{2} - 1)( \sqrt{2} + 1)} \\ \\ = \frac{ 25(\sqrt{2} + 1)}{ (\sqrt{2}) ^{2} - {(1)}^{2} )} \\ \\ = \frac{ 25(\sqrt{2} + 1)}{2 - 1} \\ \\ = \frac{ 25(\sqrt{2} + 1)}{1} \\ \\ = \boxed{25}( \boxed{1} + \sqrt{2} )[/tex]
