Question

Rationalise the denominators of the following
1
$\sqrt{3} + 1$
​

Answer 1

$\Huge\green{\underline{\fbox{\red{ \frac{ \sqrt{3} - 1}{2} }}}}$

We have,
$\huge\purple{\orange{ \mapsto } \frac{1}{ \sqrt{3} + 1} }$

$\huge\blue{ = \frac{1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1} }$

$\huge\blue{ = \frac{ \sqrt{3} - 1}{( \sqrt{3} + 1)( \sqrt{3} - 1)} }$

$\huge\blue{ = \frac{ \sqrt{3} - 1}{ {( \sqrt{3} )}^{2} - {(1)}^{2} } }$

$\huge\blue{ = \frac{ \sqrt{3} - 1}{3 - 1} }$

$\huge\blue{ = \frac{ \sqrt{3} - 1}{2} }$

$\Huge\green{\underline{\fbox{\red{\ddot\smile}}}}$$\Huge\green{\underline{\fbox{\blue{\ddot\smile}}}}$$\Huge\green{\underline{\fbox{\orange{\ddot\smile}}}}$$\Huge\green{\underline{\fbox{\pink{\ddot\smile}}}}$$\Huge\green{\underline{\fbox{\purple{\ddot\smile}}}}$