Question

6-√6 supra 6√3 - 4+3√6 supra 3√3 + √6-2 supra 4√3 - 3+√6 supra 2√2

Answer 1

(6-√6)/6√3-(4+3√6)/3√3+(√6-2)/4√3-(3+√6)/2√2=

[(6-√6)/6√3]x√3/√3=    [(6-√6)·√3]/6√3·√3=(6√3-√18)/18=(6√3-3√2)/18=3(2√3-√2)/18=(2√3-√2)/6

[(4+3√6)/3√3]x√3/√3=[ (4+3√6)·√3]/(3√3·√3)=(4√3+3√18)/9=(4√3+9√2)/9

[(√6-2)/4√3]x(√3/√3)=(√18-2√3)/(4√3·√3)=(3√2-2√3)/12

[(3+√6)/2√2]x(√2/√2)=(6√2+√12)/4=(3√2+2√3)/4

⇒ [ (2√3-√2)/6-(4√3+9√2)9+ (3√2-2√3)/12-(3√2+2√3)/4]=[12√3-6√2-16√3-36√2+9√2-6√3-27√2-18√3]/36=-(28√3-60√2)/36=-4(7√3+15√2)/36= -(7√3+15√2)/9