Question

ratonalize the denominator 1/8+5√2
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Answer 1

Answer:

$\frac{1}{8 + 5 \sqrt{2} }$

$= \frac{1}{8 + 5 \sqrt{2} } \times \frac{8 - 5 \sqrt{2} }{8 - 5 \sqrt{2} }$

$= \frac{8 - 5 \sqrt{2} }{ {(8)}^{2} - {(5 \sqrt{2}) }^{2} }$ [a²-b² = (a+b)(a-b)]

$= \frac{8 + 5 \sqrt{2} }{64 - 50}$

$= \frac{8 + 5 \sqrt{2} }{14}$