Simplify 2√2-√3 --------------- √2+√3

Madhurya Gandi asked Apr 24, 2023

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1 vote

Simplify 2√2-√3
---------------
√2+√3

Madhurya Gandi asked Apr 24, 2023

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11 votes

Explanation:

= (2 √(2) - √(3) )/( √(2) + √(3) )

= (2 √(2) - √(3) )/( √(2) + √(3) ) * ( √(2) - √(3) )/( √(2) - √(3) )

$= \frac{ 2( √(2) - √(3) )( √(2) - √(3) )}{ { √(2) }^(2) - { √(3) }^(2) }$

= (2(2 - √(6) - √(6) - 3) )/(2 - 3)

= (2( - 1 - 2 √(6) ))/( - 1)

= ( - 2(1 + 2 √(6) ))/( - 1)

= 2(1 + 2 √(6) )

= 2 + 4 √(6)

Danny Santos answered Apr 29, 2023

3.2k points

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