Question

Rationalise the denominator 1/(5+√2)​

Answer 1

✯✯ QUESTION ✯✯

Rationalise the Denominator..

$\dfrac{1}{(5+\sqrt{2}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

✰✰ ANSWER ✰✰

$\dfrac{1}{(5+\sqrt{2}}$

$⇝\dfrac{1}{5+\sqrt{2}}\times\dfrac{5-\sqrt{2}}{5-\sqrt{2}}$

$⇝\dfrac{5-\sqrt{2}}{a^2-b^2}$

$⇝\dfrac{5-\sqrt{2}}{(5)^2-(\sqrt{2)}^2}$

$⇝\dfrac{5-\sqrt{2}}{25-2}$

$\large{\boxed{\bold{\bold{\green{\sf{Answer:.\dfrac{5-\sqrt{2}}{23}}}}}}}$

Answer 2

Question:

Rationalise the denominator

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

Solution:

${ \sf {We \: will \: multiply \: the \: numerator \: and \: denominator \: with }} \\ \: (5 - \sqrt{2} )$

$= > \frac{1 \times</u></strong><strong><u> </u></strong><strong><u> (5 - \sqrt{2} )}{5 + \sqrt{2} \times (5 - \sqrt{2} )} \\ \\ = > \frac{5 - \sqrt{2} }{ {5}^{2} - ( \sqrt{2} ) {}^{2} } \: \: ({ \: \:{a {}^{2} - {b}^{2}} = (a - b)(a - b) } \: ) \\ \\ = > \frac{5 - \sqrt{2} }{25 - 2} \\ \\ = > \frac{5 - \sqrt{2} }{23}$