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

2 Answers
Nam D.
Jun 28, 2018

12+5sqrt1212+5√12

Explanation:

Given: (sqrt6+2sqrt2)(4sqrt6-3sqrt2)(√6+2√2)(4√6−3√2).

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

So, we get:

=sqrt6*4sqrt6-3sqrt2*sqrt6+2sqrt2*4sqrt6-2sqrt2*3sqrt2=√6⋅4√6−3√2⋅√6+2√2⋅4√6−2√2⋅3√2

=4*6-3sqrt12+8sqrt12-6*2=4⋅6−3√12+8√12−6⋅2

=24-12+5sqrt12=24−12+5√12

=12+5sqrt12=12+5√12

Kalyanam S.
Jun 28, 2018

color(crimson)(=> 2 (6 - 5 sqrt 3)⇒2(6−5√3)

Explanation:

(sqrt 6 + 2 sqrt 2) (4 sqrt 6 - 3 sqrt 2)(√6+2√2)(4√6−3√2)

=> sqrt 6 * 4 sqrt 6 + 2 sqrt 2 * 4 sqrt 6 - sqrt 6 * 3 sqrt 2 - 2 sqrt 2 * 3 sqrt 2⇒√6⋅4√6+2√2⋅4√6−√6⋅3√2−2√2⋅3√2

=> 4 * 6 + 8 sqrt 12 - 3 sqrt 12 - 6 * 2⇒4⋅6+8√12−3√12−6⋅2

=> 24 - 12 + 8 sqrt 12 - 3 sqrt 12⇒24−12+8√12−3√12

=> 12 + 5 sqrt (4 * 3)⇒12+5√4⋅3

=> 12 - 10 sqrt 3⇒12−10√3

color(crimson)(=> 2 (6 - 5 sqrt 3)⇒2(6−5√3)

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