Question

$sqrt{18- sqrt{288} }( sqrt{2} +1)$

Answer 1

$sqrt{18-sqrt{288}}cdot (sqrt2+1)=sqrt{18-sqrt{4cdot 72}}cdot (sqrt2+1)=\\=sqrt{18-2sqrt{6cdot 12}}cdot (sqrt2+1)=sqrt{6+12-2sqrt6cdot sqrt{12}}cdot (sqrt2+1)=\\=sqrt{(sqrt12-sqrt6)^2}cdot (sqrt2+1)=(sqrt{12}-sqrt6)cdot (sqrt2+1)=\\=sqrt6cdot (sqrt2-1)(sqrt2+1)=sqrt6cdot (2-1)=sqrt6$

Answer 2

$[tex] sqrt{18- sqrt{288} } ( sqrt{2} +1)= sqrt{12+6-12 sqrt{2} } ( sqrt{2} +1)= \ sqrt{12-2*6 sqrt{2}+6 } ( sqrt{2} +1)= sqrt{(2 sqrt{3} - sqrt{6} ) ^{2} } ( sqrt{2} +1) \ (2 sqrt{3} - sqrt{6} )( sqrt{2} +1)=2 sqrt{6} +2 sqrt{3} -2 sqrt{3} - sqrt{6} = sqrt{6}$