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Simplify √(8 - 4√3)

 Jul 27, 2021
 #1
avatar+181 
+1

Factor out $2^2$ from each of the numbers to get...

 

$\boxed{2\sqrt{2-\sqrt{3}}}$

 Jul 27, 2021
 #2
avatar+2205 
+1

Nice, but I think that it can be simplified further. 

 

sqrt(a) - sqrt(b) = sqrt(8-4sqrt(3))

a + b - 2sqrt(ab) = 8 - 4sqrt(3)

 

a + b = 8

ab = 12

a = 6, b = 2. *Note that a > b because sqrt(8-4sqrt(3)) is positive. 

 

sqrt(6) - sqrt(2) = sqrt(8-4sqrt(3))

 

=^._.^=

catmg  Jul 27, 2021

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