Step-by-step explanation:
[tex]\underline{\underline{\sf{➤ \:\: Solution }}}[/tex]
[tex] \sf\: \: \: \dfrac{1}{ \sqrt{3} - \sqrt{2} } [/tex]
On rationalising,
[tex] \sf \implies \dfrac{1}{ \sqrt{3} - \sqrt{2} } \times \dfrac{\sqrt{3} + \sqrt{2} }{\sqrt{3} + \sqrt{2} } [/tex]
Combine the fractions,
[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) } [/tex]
We know that,
[tex] \sf \implies (a - b)(a + b) = (a)^{2} - (b)^{2} [/tex]
So,
[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3})^{2} - (\sqrt{2}) ^{2} }[/tex]
[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{3 - 2 }[/tex]
[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{1 }[/tex]
[tex] \sf \implies ( \sqrt{3} + \sqrt{2}) [/tex]
Hence,
On rationalising we got,
[tex]\implies \bf (\sqrt{3} + \sqrt{2}) [/tex]
