Question

rationalise the denominators of the following 3-√3/3+√3
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Answer 1

$\huge\green {\underline {\mathfrak {Answer:}}}$

$\underline {\bold{\pink{Given:}}}$

➣$\dfrac{3-\sqrt3}{3+\sqrt3}$

➣$To \ rationalise$

$\underline {\bold {\pink{Solution:}}}$

✦$\color{gold}{Rationalizing \ denominator:}$

➫$\dfrac{3 - \sqrt3}{3 + \sqrt3}$

➫$\dfrac{3 - \sqrt3}{3 + \sqrt3} \times \dfrac{3-\sqrt3}{3 -\sqrt3}$

➫$\dfrac{(3-\sqrt3)^2}{3^2 - \sqrt3^2}$

➫$\dfrac{3 + 3 -6\sqrt3}{9 - 3}$

➫$\dfrac{6 - 6\sqrt3}{6}$

➫$\dfrac{6(1 - \sqrt3}{6}$

$\boxed{\implies{\boxed{1 - \sqrt3}}}$