Question

rationalize the denominator:
$1 \div 1 + \sqrt{5} + \sqrt{3}$

Answer 1

Hi ,

1/( 1 + √5 + √3 )

= ( 1 + √5 - √3 )/[(1+√5+√3)(1+√5-√3)]

= ( 1 + √5 - √3 )/[ ( 1 + √5 )² - ( √3 )² ]

= ( 1 + √5 - √3 )/[ 1 + 5 +2√5 - 3 ]

= ( 1 + √5 - √3 )/[ 3 + 2√5 ]

= [(1+√5-√3)(2√5 - 3 )]/[(2√5+3)(2√5-3)]

= [2√5+10-3√5-3-3√5+3√3]/[(2√5)²-3²]

= ( 7 - 4√5 +3√3 )/( 20 - 9 )

= ( 7 - 4√5 + 3√3 )/11

I hope this helps you.

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