Question

Срочно! Упростите выражение  $sqrt{109+12sqrt{3}}-sqrt{109-12sqrt{3} }$

Answer 1

$sqrt{109+12sqrt{3} } -sqrt{109-12sqrt{3} }=sqrt{1+12sqrt{3}+108 }-sqrt{1-12sqrt{3}+108 }=sqrt{(1+6sqrt{3})^{2}}-sqrt{(1-6sqrt{3})^{2} }=|1+6sqrt{3}|-|1-6sqrt{3}|=1+6sqrt{3}-(6sqrt{3}-1)=1+6sqrt{3}-6sqrt{3} +1=2$