Question

7√3-5√2÷√48+√18 rationaise the denominator​

Answer 1

Answer:

Refer the above pic for answer

Answer 2

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Step-by-step explanation:

$\huge\boxed{{\bf { \ given \: \: \: \frac{(7 \sqrt{3} - 5 \sqrt{2} ) }{( \sqrt{48} + \sqrt{18} } }}}$

$\huge\boxed{{\bf { = \frac{(7 \sqrt{3} - 5 \sqrt{2}) }{( \sqrt{4} \times 4 \times 3 \times \sqrt{3} \times 3 \times 2} }}}$

$\huge\boxed{{\bf { = \frac{(7 \sqrt{3} - 5 \sqrt{2} }{(4 \sqrt{3} + 3 \sqrt{2} } }}}$

$\huge\boxed{{\bf {Multiplying \: \: numerator \: \: and \: \: denominator \: \: by \: \: (4 \sqrt{3} - 3 \sqrt{2} ) \: we \: get }}}$

$\huge\boxed{{\bf { = \frac{(7 \sqrt{3 } - 5 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} }{(4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} )} }}}$

$\huge\boxed{{\bf { = \frac{28 \times 3 - 21 \sqrt{6} - 20 \sqrt{6} + 15 \times 2}{(4 { \sqrt{3} )}^{2} - {(3 \sqrt{2} )}^{2} } }}}$

$\huge\boxed{{\bf { = \frac{84 - 41 \sqrt{6} + 30 }{48 - 18} }}}$

$\huge\boxed{{\bf { = \frac{114 - 41 \sqrt{6} }{30} }}}$

$\huge\boxed{{\bf {Denominator \: \: rationalised }}}$

$\huge\boxed{{\bf { Therefore, }}}$

$\huge\boxed{{\bf { \frac{(7 \sqrt{3} - 5 \sqrt{2}) }{ (\sqrt{48} + \sqrt{18} ) } }}}$

$\huge\boxed{{\bf { = \frac{114 - 41 \sqrt{6} }{30} }}}\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \huge\boxed{{\bf { answer}}}$