Question

（根号18加2根号3加3根号6 ）分之根号6加4根号3加3根号2

化简
是分之（根号6加4根号3加3根号2）

Answer 1

(√6+4√3+3√2)/(√18+2√3+3√6)
=(√6+4√3+3√2)/(3√2+2√3+3√6)
=(√6+4√3+3√2)(2√3+3√6-3√2)/(3√2+2√3+3√6)(2√3+3√6-3√2)
=(2√18+18-3√12+24+12√18-12√6+6√6+9√12-18)/[(2√3+3√6)²-(3√2)²]
=(7√2+2√3+4-√6)/(8+6√2)
=(7√2+2√3+4-√6)(8-6√2)/(8+6√2)(8-6√2)
=(56√2-84+8√3-12√6+32-24√2-8√6+6√12)/(64-72)
=(32√2-52+20√3-20√6)/(-8)
=-(8√2-13+5√3-5√6)/2