Question

rationalize the denominator​

Answer 1

$\huge{\underline{\underline{\mathfrak{Solution :}}}}$

$\sf{\longrightarrow \dfrac{3\sqrt{3} - 2\sqrt{5}}{3\sqrt{3} + 2\sqrt{5}}}$

$\sf{\longrightarrow \dfrac{3\sqrt{3} - 2\sqrt{5}}{3\sqrt{3} + 2\sqrt{5}} \times \dfrac{3\sqrt{3} - 2\sqrt{5}}{3\sqrt{3} - 2\sqrt{5}}}$

$\bf{\underline{\bigstar Using\ identity }}$

${\boxed{\boxed{\sf{(a - b) \times (a + b) = a^2 - b^2}}}}$

$\sf{\longrightarrow \dfrac{(3\sqrt{3})^2 + (2\sqrt{5})^2 - 2(3\sqrt{3})(2\sqrt{5})}{(3\sqrt{3})^2 - (2\sqrt{5})^2}}$

$\sf{\longrightarrow \dfrac{27 + 20 - 12\sqrt{15}}{27 - 20}}$

$\sf{\longrightarrow \dfrac{47 - 12\sqrt{15}}{7}}$