Question

rationalize the denominator and simplify 2/,5√3-2√2​

Answer 1

$\dfrac{2}{5\sqrt{3} - 2\sqrt{2} }\\\\=(\dfrac{2}{5\sqrt{3} - 2\sqrt{2} } )(\dfrac{5\sqrt{3} + 2\sqrt{2}}{5\sqrt{3} + 2\sqrt{2}})\\\\=\dfrac{10\sqrt{3} + 4\sqrt{2}}{(5\sqrt{3})^2 - (2\sqrt{2})^{2}}..[a^{2} - b^{2} = (a+b)(a-b)]\\\\=\dfrac{10\sqrt{3} + 4\sqrt{2}}{(25)(3) - (4)(2)}\\\\=\dfrac{10\sqrt{3} + 4\sqrt{2}}{75 - 8}\\\\=\dfrac{10\sqrt{3} + 4\sqrt{2}}{67}$