Question

√3+√2 upon√3-√2 solve this the question is rationlise the denominator​

Answer 1

Answer: 5 + 2√6

(✓3 + √2) / (√3 - √2)

Rationalising the denominator,

Multiplying the numerator and denominator by ✓3+√2/√3+√2 ,

(✓3 + √2) / (√3 - √2) × (√3 + √2) / (√3 + √2)

=> (√3 + √2) (√3 + √2) / (√3)² - (√2)²

=> (√3 + √2)² / 3 - 2

=> 3 + 2 + 2(√3)(√2) / 1

=> 5 + 2√6 / 1

=> 5 + 2√6

thus, the answer is 5 + 2√6.

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

${ \star \: {\sf{\green{ \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } }}}}$

${\sf{\underline{\blue{Now,}}}}</p><p>$

${\tt \implies{ \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }}$

${\bf{\blue{\underline {\boxed {(x + y) (x - y)= {x}^{2} - {y}^{2} }}}}}$

${\tt \implies{ \frac{ (\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2} ) }{( { \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } }}$

${\tt \implies{ \frac{3 + \sqrt{3} \sqrt{2} + \sqrt{2} \sqrt{3} + 2 }{3 - 2} }}$

${\tt \implies{ \frac{3 + 2 \times \sqrt{3 \times 2} + 2 }{1} }}$

${\tt \implies{ {3 + 2 \times \sqrt{6} + 2 } }}$

${\tt \implies{ {5+ 2 \times \sqrt{6} } }}$

${\tt \implies{ {5+ 2 \: \sqrt{6} \: Ans } }}$