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# help

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Simplify √(8 - 4√3)

Jul 27, 2021

#1
+181
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Factor out $2^2$ from each of the numbers to get...

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

Jul 27, 2021
#2
+2193
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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