How do you simplify (sqrt2) + 2 (sqrt2) + (sqrt8) / (sqrt3)?

2 Answers
Sonnhard
Jul 12, 2018

sqrt(2)/3(9+2sqrt(3))

Explanation:

sqrt(2)+2*sqrt(2)+2sqrt(2)/sqrt(3)
since sqrt(8)=2sqrt(2)

(sqrt(2)`sqrt(3)+2*sqrt(2)*sqrt(3)+2sqrt(2))/sqrt(3)

multiplying numerator and denominator by sqrt(3)

sqrt(2)/3(3+2*3+2*sqrt(3))

and this is

sqrt(2)/3(9+2*sqrt(3))

Meave60
Jul 12, 2018

sqrt2+2sqrt2+(sqrt8)/(sqrt3)=color(blue)(3sqrt2+(2sqrt6)/3

Explanation:

Simplify:

sqrt2+2sqrt2+(sqrt8)/(sqrt3)

Simplify sqrt8.

sqrt2+2sqrt2+(sqrt(2xx2xx2))/(sqrt3)

sqrt2+2sqrt2+(sqrt(2^2xx2))/(sqrt3)

Apply square root rule: sqrt(a^2)=a

sqrt2+2sqrt2+(2sqrt2)/(sqrt3)

Rationalize the denominator by multiplying the numerator and denominator by sqrt3.

sqrt2+2sqrt2+(2sqrt2sqrt3)/(sqrt3sqrt3)

Apply square root rule: sqrtasqrta=a

sqrt2+2sqrt2+(2sqrt2sqrt3)/3

Apply square root rule: sqrtasqrtb=sqrt(ab)

sqrt2+2sqrt2+(2sqrt6)/3

Simplify.

3sqrt2+(2sqrt6)/3

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