rationalise the denominator of 4 root 3+5 root 2 divided by root 48 +root 18

43+5248+18= 43+524×4×3+3×3×2= 43+5243+32= 43+5243+32×43-3243-32  {rationalising the denominator}= 4343-32+5243-32432-322= 48-126+206-3048-18= 18+8630= 29+4630= 9+4615

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(4√3 + 5√2) ÷ (√48 + √18)

= (4√3 + 5√2)(√48 - √18) ÷ (√48 + √18)(√48 - √18) [ Multiplying numerator and denominator by the rationalising factor. ie. (√48 - √18) ]

= ( (4√3 x √48) + (4√3 x-√18) + (5√2 x √48) + (5√2 x -√18) ) ÷ ( (√48)2 - (√18)2 ) [Since, (a+b)(a-b) = a2 - b2]

= ( 4√144 - 4√54 + 5√96 - 5√36 ) ÷ ( 48 - 18 )

= ( 4 x 12 - 4√54 + 5√96 - 5 x 6 ) ÷ 30

= (48 - 4√54 + 5√96 -30) ÷ 30

= (18 - 4√54 + 5√96) ÷ 30

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Hope this would have cleared your doubt . 

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