Question

Rationalize the denominator:

(a) 2/(√3−1)​

Answer 1

$\sf\color{blue}\bigstar{Answer}\bigstar$

$\color{red}\longrightarrow{}$$\sqrt{3} + 1$

$\sf\color{green}\bigstar{Step\:-by\:-step\: explanation}\bigstar$

$\color{red}\longrightarrow{}$$\frac{2}{ \sqrt{3} - 1}$

$\rm\color{orchid}\bigstar{Rationalising \:the\: denominator}\bigstar$

$\color{red}\longrightarrow{}$$\frac{2}{ \sqrt{3} - 1 } \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1}\frac{2( \sqrt{3} + 1)}{ { \sqrt{3} }^{2} - {1}^{2} }$

$\color{red}\longrightarrow{}$$\frac{2 \sqrt{3} + 2}{3 - 1}$

$\color{red}\longrightarrow{}$$\frac{2( \sqrt{3} + 1)}{2}$

$\color{red}\longrightarrow{}$$\sqrt{3} + 1$

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Thankyou :)

Refer attachment for better understanding :)