Question

show that (4+√8)/(√2-1) can be written in the form a+b√2 where a and b are integers.

Answer 1

Answer:

GIVES THAT-

$\frac{4 + \sqrt{8} }{ \sqrt{2} - 1}$

RATIONALIZATION -

$= \frac{4 + \sqrt{8} }{ \sqrt{2} - 1 } \times \frac{ \sqrt{2} + 1}{ \sqrt{2} + 1 } \\ \\ = \frac{2 \sqrt{2} {( \sqrt{2} + 1) }^{2} }{2 - 1} \\ \\ = (2 \sqrt{2} )(2 + 1 + 2 \sqrt{2} ) \\ \\ = 6 \sqrt{2} + 8$

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