Question

Rationalize the denominator.
1 / (√7 +√2 ) (ii) 1 / (32√5 - 3√2)​

Answer 1

Question -

Rationalize the denominator

$1)\sf \frac{1}{ \sqrt{7} + \sqrt{2} }$

$2)\sf \frac{1}{32 \sqrt{5} - 3 \sqrt{2} }$

Solution -

$1) \bf\dfrac{1}{ \sqrt{7} + \sqrt{2} }$

$= \bf\dfrac{ \sqrt{7} - \sqrt{2} }{( \sqrt{7} + \sqrt{2} )( \sqrt{7} - \sqrt{2} )}$

$= \bf\dfrac{ \sqrt{7} - \sqrt{2} }{ {( \sqrt{7} )}^{2} - {( \sqrt{2}) }^{2} }$

$= \bf \dfrac{ \sqrt{7} - \sqrt{2} }{7 - 2}$

$= \bf \dfrac{ \sqrt{7} - \sqrt{2} }{5}$

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$2) \bf\dfrac{1}{32 \sqrt{5} - 3 \sqrt{2} }$

$= \bf\dfrac{32 \sqrt{5} + 3 \sqrt{2} }{(32 \sqrt{5} - 3 \sqrt{2})(32 \sqrt{5} + 3 \sqrt{2}) }$

$= \bf\dfrac{32 \sqrt{5} + 3 \sqrt{2} }{ ({32 \sqrt{5}) }^{2} - ( {3 \sqrt{2}) }^{2} }$

$= \bf \dfrac{32 \sqrt{5} + 3 \sqrt{2} }{5120 - 18}$

$= \bf \dfrac{32 \sqrt{5} + 3 \sqrt{2} }{5102}$

Answer 2

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=> √3 - √2 / √3 + √2 x √3 - √2/√3 - √2

=> (√3 - √2)^2/(√3)^2 - (√2)^2

[a-b]^2= a^2+b^2-2ab

=> (√3)^2 +(√2)^2-2.√3.√2/3-2

=> 3+2-2√6/1

=> 5-2√6

In this type of questions, at first we multiply the denominators and numerators by opposite sign and same as number given in denominators.

After, that with proper calculation we find out our results.