Question

rationalize the denominator
4
$4 \sqrt{3} + 5 \sqrt{2} \div \sqrt{48} - \sqrt{18}$
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Answer 1

$\frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{48} - \sqrt{18} } \\ \\ \frac{4 \sqrt{3} + 5 \sqrt{2} ( \sqrt{48} + \sqrt{18} ) }{ {( \sqrt{48} )}^{2} - {( \sqrt{18} )}^{2} } \\ \\ \frac{4 \sqrt{144} + 4 \sqrt{54} + 5 \sqrt{96} + 5 \sqrt{36} }{48 - 18} \\ \\ \frac{4(12) + 12 \sqrt{6} + 20 \sqrt{6} + 5(6)}{30} \\ \\ \frac{48 + 30 + 32 \sqrt{6} }{30} \\ \\ \frac{78 + 32 \sqrt{6} }{30} \\ \\ \frac{2(39 + 16 \sqrt{6} )}{30} \\ \\ \frac{39 + 16 \sqrt{6} }{15}$

Answer 2

Answer:

(9+4√6)/15

Step-by-step explanation:

4√3+5√2/√48-√18

=4√3+5√2/4√3-3√2

=(4√3+5√2)(4√3-3√2)/(4√3-3√2)(4√3+3√2)

=(48-30-12√6+20√6)/48-18

=1/30(18+8√6)

=2/30(9+4√6)

=(9+4√6)/15