Question

Rationalise(3 - √6) / (6- √3)​

Answer 1

$\sf{{\dfrac{3-{\sqrt{6}}}{6-{\sqrt{3}}}}}$

multiply $\sf{\bold{{6+{\sqrt{3}}}}}$ in numerator and denominator .

$\sf{={\dfrac{(3-{\sqrt{6}})(6+{\sqrt{3}})}{(6-{\sqrt{3}})(6+{\sqrt{3}})}}}$

${\boxed{\sf{\bold{\footnotesize{(3-{\sqrt{6}})(6+{\sqrt{3}})= 18+3{\sqrt{3}} - 6{\sqrt{6}} -3{\sqrt{2}}}}}}}$

${\boxed{\sf{\bold{\footnotesize{(6-{\sqrt{3}})(6+{\sqrt{3}}) = 33}}}}}$

$\sf{={\dfrac{18+3{\sqrt{3}} - 6 {\sqrt{6}}-3{\sqrt{2}}}{33}}}$

$\boxed{\sf{\bold{\footnotesize{factor~{18+3{\sqrt{3}}-6{\sqrt{6}}-3{\sqrt{2}}} ⇒3(6+{\sqrt{3}} - 2{\sqrt{6}} - {\sqrt{2}}}}}}$

$\sf{={\dfrac{3(6+{\sqrt{3}} - 2{\sqrt{6}} - {\sqrt{2}})}{33}}}$

Cancel the common factor 3

$\sf{\boxed{\boxed{={\dfrac{(6+{\sqrt{3}} - 2{\sqrt{6}} - {\sqrt{2}})}{11}}}}}$