How do you simplify (12+sqrt108)/6?

2 Answers
EZ as pi
May 29, 2017

= 2+sqrt3

Explanation:

Each term in the numerator must be divided by 6:

(12+sqrt108)/6 = 12/6+sqrt108/6" "larr prime factor 108

=2+ sqrt(2xx2xx3 xx3xx3)/6 = 2+sqrt(2^2xx3^2xx3)/6

Find the roots where possible.

2+(2*3sqrt3)/6 = 2+(cancel6sqrt3)/cancel6

= 2+sqrt3

Jim G.
May 29, 2017

2+sqrt3

Explanation:

"simplifying " sqrt108" to begin with"

"using the "color(blue)"law of radicals"

color(orange)"Reminder " sqrtaxxsqrtbhArrsqrt(ab)

rArrsqrt108=sqrt(2^2xx3^3)=2xx3sqrt3=6sqrt3

rArr(12+sqrt108)/6

=(12+6sqrt3)/6

=12/6+(6sqrt3)/6

=2+sqrt3

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