3√5/12 + √21/5 – 1/3 √60?

3(sqrt((5/(3x4))) + sqrt(21/5) - 1/3 x sqrt (2 x 2 x 15)=

(3sqrt(5/3))/2 + sqrt(21/5) -1/3 x 2 x sqrt (15)=

3/2(sqrt(5/3)) + sqrt (21/5) -2/3 x sqrt (15)

is the first term...

3√(5/12) or (3√5)/12

is that last term...

– (1/3) √60 ... as in -√60/3

or - 1/(3√60)

it makes a difference on the final answer which these two are.

assuming for the easiest:

(3√5)/12 +(√21)/5 –(√60)/3

common factor for the denominators (12, 5, and 3) is 60

putting this into a common form:

5(3√5)/60 +12(√21)/60 –20(√60)/60

simplifies down to:

[5(3√5) +12(√21) –20(√60)] / 60

[ 15√5 +12√(3.7) –20√(2.2.5)] / 60

[ 15√5 +12√(3.7) –40√(5)] / 60

[ 15√5 –40√(5) +12√(3.7)] / 60

[ -25√(5) +12√(3.7)] / 60

ANS: (12√21 -25√5) / 60 ... this could be re-written as (√21)/5 - (5√5)/12

√3 *√(3*5/12)+√3*√(3/7) -√3√(60/9)

√3(5/4+3/7-20/3)

√3(-419/84)