Math, asked by aadi615, 11 months ago

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

Answers

Answered by DevyaniKhushi
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}

Answered by Anonymous
1

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

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