Question

rationalise √3+√2/√3-√2​

Answer 1

Answer:

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = \frac{( \sqrt{3} + \sqrt{2} )( \sqrt{3} + \sqrt{2}) }{3 - 2} \\ = \frac{(3 + 2 + 2 \sqrt{6}) }{1} \\ = 5 + 2 \sqrt{6}$

Answer 2

Given:  

(√3+ √2) /  (√3- √2)

We can rationalise the denominator by multiplying numerator and denominator by  (√3+ √2 )

Answer:

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

=> (√3+√2)(√3+√2) / (√3-√2)(√3+√2)

{ using (a+b)²= a²+b²+2ab } &

{ a²-b²= (a+b) (a-b) }

=> (√3+√2)²/ (√3)²-(√2)²

=> (√3)²+(√2)²+2(√3)(√2) / 3-2

=> (3+2+2√6) / 1

=> 5+2√6

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