Question

Упростить выражение.

Answer 1

$sqrt{22+6 sqrt{3+ sqrt{(2 sqrt{3}+1)^2 } } } = sqrt{22+6 sqrt{3+2 sqrt{3}+1 } } =$$sqrt{22+6 sqrt{( sqrt{3}+1)^2 } } = sqrt{22+6( sqrt{3} +1)}= sqrt{22+6 sqrt{3}+6 }$$= sqrt{28+6 sqrt{3} } = sqrt{(3 sqrt{3}+1)^2 }=3 sqrt{3} +1$

Answer 2

$sqrt{22+6 sqrt{3+ sqrt{13+ sqrt{48}}}} = sqrt{22+6 sqrt{3+ sqrt{13+ sqrt{4^2bullet3}}}} =\\= sqrt{22+6 sqrt{3+ sqrt{12+ 4sqrt{3}+1}}} =sqrt{22+6 sqrt{3+ sqrt{(sqrt{12}+1)^2}}} =\\=sqrt{22+6 sqrt{3+ sqrt{12}+1}}}=sqrt{22+6 sqrt{3+ 2sqrt{3}+1}}}=\\=sqrt{22+6 sqrt{(sqrt3+1)^2}}}=sqrt{22+6 (sqrt3+1)}}}=sqrt{28+6sqrt3}=\\=sqrt{27+6sqrt3+1}=sqrt{(sqrt{27}+1)^2}=sqrt{27}+1=3sqrt3+1.$