Question

reationalise the denominator √3+√2
______
√3-√2​

Answer 1

⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Le \:Answer★}}}}}$

√3-√2 × √3 +√2

(√3)² - (√2)²

3 - 2

1

Answer 2

Step-by-step explanation:

Correct Question:-

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

Solution:-

Let's solve the problem

We have,

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

The denominator is √3-√2. Multiplying the numerator and denomination by √3+√2, we get

$⟹ \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

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

⬤ Applying Algebraic Identity

✯(a+b)² = a² + b² + 2ab to numerator and

✯(a-b)(a+b) = a² - b² to the denominator

Weget,

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

$⟹ \frac{( \sqrt{3} {)}^{2} + ( \sqrt{2} {)}^{2} + 2 \sqrt{3 \times 2} }{3 - 2}$

$⟹ \frac{3 + 2 + 2 \sqrt{3 \times 2} }{1}$

$⟹ \frac{5 + 2 \sqrt{6} }{1}$

$⟹5 + 2 \sqrt{6}$

Hence, the denominator is rationalised.

Answer:-

$5 + 2 \sqrt{6}$

Used Formulae:-

• (a+b)² = a² + b² + 2ab

• (a-b)(a+b) = a² - b²