Simplify the following by rationalising the denominator.Plz answer thi

1.	Simplify the following by rationalising the denominator.Plz answer this question plz plz.
Answer» ONG>Step-by-step explanation: QUESTION:- Solve the following by RATIONALIZING the denominator:- $\sf(i) \: \dfrac{1}{3 \sqrt{2} - 2 \sqrt{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (ii) \: \dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} }$ Solution:- $\sf(i) \: \: \dfrac{1}{3 \sqrt{2} - 2 \sqrt{3} }$ By rationalizing the denominator:- $\sf = \dfrac{1}{3 \sqrt{2} - 2 \sqrt{3} } \times \dfrac{3 \sqrt{2} + 2\sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3}}$ $\sf = \dfrac{3 \sqrt{2} + 2\sqrt{3} }{(3 \sqrt{2})^{2} - (2 \sqrt{3})^{2} }$ $\sf = \dfrac{3 \sqrt{2} + 2\sqrt{3} }{ }$ $\sf = \dfrac{3 \sqrt{2} + 2\sqrt{3} }{6 }$ $\underline{\boxed{\bf \leadsto \dfrac{3 \sqrt{2} + 2\sqrt{3} }{6 }}}$ ________________________ $(ii) \: \dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} }$ By rationalizing the denominator:- $\sf = \dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} } \times \dfrac{3 \sqrt{3} - \sqrt{2} }{3 \sqrt{3} - \sqrt{2} }$ $\sf = \dfrac{3 \sqrt{5}( 3 \sqrt{3} - \sqrt{2}) - \sqrt{7}(3 \sqrt{3} - \sqrt{2}) }{(3 \sqrt{3} - \sqrt{2} )(3 \sqrt{3} + \sqrt{2}) }$ $\sf = \dfrac{3 \sqrt{5}( 3 \sqrt{3}) - 3 \sqrt{5} (\sqrt{2}) - \sqrt{7}(3 \sqrt{3} ) - \sqrt{7}( \sqrt{2}) }{(3 \sqrt{3})^{2} - (\sqrt{2} )^{2} }$ $\sf = \dfrac{9 \sqrt{15}- 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14} }{27 - 2 }$ $\sf = \dfrac{9 \sqrt{15}- 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14} }{25 }$ $\underline{\boxed{\bf \leadsto \dfrac{9 \sqrt{15}- 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14} }{25 } }}$

Simplify the following by rationalising the denominator.Plz answer this question plz plz.

Answer» ONG>Step-by-step explanation:

QUESTION:-

Solve the following by RATIONALIZING the denominator:-

$\sf(i) \: \dfrac{1}{3 \sqrt{2} - 2 \sqrt{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (ii) \: \dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} }$

Solution:-

$\sf(i) \: \: \dfrac{1}{3 \sqrt{2} - 2 \sqrt{3} }$

By rationalizing the denominator:-

$\sf = \dfrac{1}{3 \sqrt{2} - 2 \sqrt{3} } \times \dfrac{3 \sqrt{2} + 2\sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3}}$

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

$\sf = \dfrac{3 \sqrt{2} + 2\sqrt{3} }{ }$

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

$\underline{\boxed{\bf \leadsto \dfrac{3 \sqrt{2} + 2\sqrt{3} }{6 }}}$

________________________

$(ii) \: \dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} }$

By rationalizing the denominator:-

$\sf = \dfrac{3 \sqrt{5} - \sqrt{7} }{3 \sqrt{3} + \sqrt{2} } \times \dfrac{3 \sqrt{3} - \sqrt{2} }{3 \sqrt{3} - \sqrt{2} }$

$\sf = \dfrac{3 \sqrt{5}( 3 \sqrt{3} - \sqrt{2}) - \sqrt{7}(3 \sqrt{3} - \sqrt{2}) }{(3 \sqrt{3} - \sqrt{2} )(3 \sqrt{3} + \sqrt{2}) }$

$\sf = \dfrac{3 \sqrt{5}( 3 \sqrt{3}) - 3 \sqrt{5} (\sqrt{2}) - \sqrt{7}(3 \sqrt{3} ) - \sqrt{7}( \sqrt{2}) }{(3 \sqrt{3})^{2} - (\sqrt{2} )^{2} }$

$\sf = \dfrac{9 \sqrt{15}- 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14} }{27 - 2 }$

$\sf = \dfrac{9 \sqrt{15}- 3 \sqrt{10} - 3 \sqrt{21} - \sqrt{14} }{25 }$