 | 1/(√6+√7)=(√7-√6)/{(√7+√6)(√7-√6)}=√7-√6
1/(√7+3)=(3-√7)/{(3+√7)(3-√7)}=(3-√7)/2
1/(3+2√3)=(2√3-3)/{(2√3+3)/(2√3-3)}=(2√3-3)/3
1/(2√3+4)=(4-2√3)/{(4+2√3)/(4-2√3)}=(4-2√3)/4=(2-√3)/2
∴
(与式)={√7-√6+(3-√7)/2+(2√3-3)/3+(2-√3)/2}^2
=(1/6^2)(6√7-6√6+9-3√7+4√3-6+6-3√3)^2
=(1/36)(3√7-6√6+√3+9)^2
=(1/36)(63+216+3+81-36√42+6√21+54√7-36√2-108√6+18√3)
=(363-36√42+6√21+54√7-108√6+18√3-36√2)/36
=(121-12√42+2√21+18√7-36√6+6√3-12√2)/12
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