How do you simplify $(8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2])$ ?

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Answer 1 · 2017-12-01T19:31:22

Use binomial multiplication (FOIL)

Going directly to the solution and not rewriting the problem, binomial multiplication gives:

$8sqrt6*4sqrt6-8sqrt6*5sqrt2+3sqrt2*4sqrt6-3sqrt2*5sqrt2$

Simplifying:
$32sqrt6^2-40sqrt12+12sqrt12-15sqrt2^2$

Next:
$32*6-28sqrt12-15*2$

$192-28sqrt12-30$

$162-28sqrt12$

Then simplify $sqrt12=sqrt{4*3}=2sqrt3$

So, $162-28*2sqrt3 = 162-56sqrt3$

How do you simplify (8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2])(8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2])?