Question

rationalize the denominator of 1 by 5 + 3 root 2​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

$\bold{What\: is \:Rationalising\: ?}$

Rationalising means removing root values from the denominator and shifting towards numerator.

Note:-There is always identity used in the denominator in most cases.

$= > \frac{1}{5 + 3 \sqrt{2} }$

$= > \frac{1}{5 + 3 \sqrt{2} } \times \frac{5 - 3 \sqrt{2} }{5 - 3 \sqrt{2} }$

Here,this identity is used:-

$\bold{\boxed{\purple{(x + y)(x - y) = {x}^{2} - {y}^{2} }}}$

$= > \frac{5 - 3 \sqrt{2} }{ {(5)}^{2} - {(3 \sqrt{2} )}^{2} }$

$= > \frac{5 - 3 \sqrt{2} }{25 - 18}$

$\bold{= > \frac{5 - 3 \sqrt{2} }{7} }$

$\bold\fcolorbox{aqua}{orange}{Answer}$$\bold{ \frac{5 - 3 \sqrt{2} }{7} }$

Answer 2

Question :

Rationalise the denominator of - $\frac{1}{5+3\sqrt{2} }$

Answer :

$\frac{1}{5+3\sqrt{2} } \\\\\implies\frac{1}{5+3\sqrt{2} }*\frac{5+3\sqrt{2} }{5+3\sqrt{2} } \\\\\implies \frac{5+3\sqrt{2} }{25+18} \\\\\implies\boxed{\frac{5+3\sqrt{2} }{43} }$

HOPE IT HELPS !!!