Question

Rationalise the denominator of the following​

Answer 1

Answer:

2 + √3

Step-by-step explanation:

$\frac{\sqrt{3}+1 }{\sqrt{3}- 1 }$

= √3 + 1 (√3 + 1) / √3 - 1 (√3 + 1)

= 3 + 2√3 + 1 / 3 - 1

= 4 + 2√3 / 2

= 2 + √3

Answer 2

Answer:

2 + √3

Step-by-step explanation:

Multiply the expression by $\dfrac{\sqrt{3} +1}{\sqrt{3} +1}$ :

$\implies \dfrac{\sqrt{3} +1}{\sqrt{3} -1}\times\dfrac{\sqrt{3} +1}{\sqrt{3} +1}=\dfrac{(\sqrt{3} +1)^2}{3+\sqrt{3}-\sqrt{3}-1}=\dfrac{(\sqrt{3} +1)^2}{2}$

$\implies \dfrac{(\sqrt{3} +1)^2}{2}=\dfrac{3+2\sqrt{3}+1 }{2}=\dfrac{4+2\sqrt{3} }{2}=2+\sqrt{3}$