How do you simplify $(sqrt [6] + 2sqrt [2])(4sqrt[6] - 3sqrt2)$ ?

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Answer 1 · 2018-06-28T13:22:53

$12+5sqrt12$

Given: $(sqrt6+2sqrt2)(4sqrt6-3sqrt2)$ .

Use the $"FOIL"$ theorem, which states that $(a+b)(c+d)=ac+ad+bc+bd$ .

So, we get:

$=sqrt6*4sqrt6-3sqrt2*sqrt6+2sqrt2*4sqrt6-2sqrt2*3sqrt2$

$=4*6-3sqrt12+8sqrt12-6*2$

$=24-12+5sqrt12$

$=12+5sqrt12$

Answer 2 · 2018-06-28T13:26:36

$color(crimson)(=> 2 (6 - 5 sqrt 3)$

$(sqrt 6 + 2 sqrt 2) (4 sqrt 6 - 3 sqrt 2)$

$=> sqrt 6 * 4 sqrt 6 + 2 sqrt 2 * 4 sqrt 6 - sqrt 6 * 3 sqrt 2 - 2 sqrt 2 * 3 sqrt 2$

$=> 4 * 6 + 8 sqrt 12 - 3 sqrt 12 - 6 * 2$

$=> 24 - 12 + 8 sqrt 12 - 3 sqrt 12$

$=> 12 + 5 sqrt (4 * 3)$

$=> 12 - 10 sqrt 3$

$color(crimson)(=> 2 (6 - 5 sqrt 3)$

How do you simplify (sqrt [6] + 2sqrt [2])(4sqrt[6] - 3sqrt2)(sqrt [6] + 2sqrt [2])(4sqrt[6] - 3sqrt2)?