Math, asked by Momomaringa, 9 months ago

Rationale the denominator and simplify 2√6-5/3√5-2√6

Answers

Answered by Anonymous

$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

To Find :

We have to rationalize

$\sf{\frac{ 2\sqrt{6} - 5}{3\sqrt{5} - 2\sqrt{6}}}$

Solution :

We know that,

When we rationalize a number then we multiply denominator by numerator and both denominator by changing the last sign.

Now,

$\rule{200}{2}$

$\sf{ \implies\frac{2 \sqrt{6} - 5}{3 \sqrt{5} - 2 \sqrt{6} } \times \frac{3 \sqrt{5} + 2 \sqrt{6} }{3 \sqrt{5} + 2 \sqrt{6} } } \\ \\ { \LARGE{ \leadsto{ \boxed{ \boxed{ \green{ \sf{{a}^{2} - {b}^{2} = (a + b)(a - b) }}}}}}} \\ \\ \bf{\hookrightarrow {Putting \: values}}\\ \\ \sf{\implies \frac{2 \sqrt{6} - 5(3 \sqrt{5} + 2 \sqrt{6} ) }{ {(3 \sqrt{5}) }^{2} - (2 \sqrt{6})^{2} } } \\ \\ \sf{\implies \frac{6 \sqrt{30} + 24 - 15 \sqrt{5} - 10 \sqrt{6}}{45 - 24}} \\ \\ \sf{\implies \frac{6 \sqrt{2 \times 3 \times 3} + 24 - 15 \sqrt{5} - 10 \sqrt{6} }{21} } \\ \\ \sf{\implies \frac{18 \sqrt{2 } + 24 - 15 \sqrt{5} - 10 \sqrt{6} }{21} }$

${ \LARGE{ \leadsto{ \boxed{ \boxed{ \blue{ \sf{\frac{18 \sqrt{2 } + 24 - 15 \sqrt{5} - 10 \sqrt{6} }{21}}}}}}}}$

Answered by lucky997761

$<body bgcolor="black"></p><p><font color="white">$

=>To Find :

=>We have to rationalize

$\sf{\frac{ 2\sqrt{6} - 5}{3\sqrt{5} - 2\sqrt{6}}}$

☆SolutiOn :

=>We know that,

➡When we rationalize a number then we multiply denominator by numerator and both denominator by changing the last sign.

➡Now,

$\begin{lgathered}\sf{ \implies\frac{2 \sqrt{6} - 5}{3 \sqrt{5} - 2 \sqrt{6} } \times \frac{3 \sqrt{5} + 2 \sqrt{6} }{3 \sqrt{5} + 2 \sqrt{6} } } \\ \\ { \LARGE{ \leadsto{ \boxed{ \boxed{ \green{ \sf{{a}^{2} - {b}^{2} = (a + b)(a - b) }}}}}}} \\ \\ \bf{\hookrightarrow {Putting \: values}}\\ \\ \sf{\implies \frac{2 \sqrt{6} - 5(3 \sqrt{5} + 2 \sqrt{6} ) }{ {(3 \sqrt{5}) }^{2} - (2 \sqrt{6})^{2} } } \\ \\ \sf{\implies \frac{6 \sqrt{30} + 24 - 15 \sqrt{5} - 10 \sqrt{6}}{45 - 24}} \\ \\ \sf{\implies \frac{6 \sqrt{2 \times 3 \times 3} + 24 - 15 \sqrt{5} - 10 \sqrt{6} }{21} } \\ \\ \sf{\implies \frac{18 \sqrt{2 } + 24 - 15 \sqrt{5} - 10 \sqrt{6} } {21} } \end {lgathered}$

${ \LARGE{ \leadsto{ \boxed{ \boxed{ \blue{ \sf{\frac{18 \sqrt{2 } + 24 - 15 \sqrt{5} - 10 \sqrt{6} }{21}}}}}}}}⇝$

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