Question

упростить

 

 

$sqrt[8]{97-56sqrt{3}}$

Answer 1

= ∜((√48)-7)=∜-(√3-2)^2=√(2-√3)=√(√3-1)^2/2=(√3-1)/√2=(√6-√2)/2

Answer 2

$sqrt[8] {97-56sqrt{3}}=\ sqrt[8] {48-56sqrt{3}+49}=\ sqrt[8] {(4sqrt{3})^2-2*(4sqrt{3})*7+7^2}=\ sqrt[8] {((4sqrt{3})^2-7)^2}=\ sqrt[4] {|4sqrt{3}-7|}=\ sqrt[4] {7-4sqrt{3})}=\ sqrt[4] {4-4sqrt{3})+3}=\ sqrt[4] {2^2-2*2*sqrt{3})+(sqrt{3})^2}=\ sqrt[4] {(2-sqrt{3})^2}=\ sqrt {|2-sqrt{3}|}=$

$sqrt {2-sqrt{3}}=\ frac{sqrt{(2-sqrt{3})*sqrt{2}}}{sqrt{2}}=\ frac{sqrt {4-2sqrt{3}}*sqrt{2}}{2}=\ frac{(sqrt {1-2sqrt{3}+3})*sqrt{2}}{2}=\ frac{(sqrt {1^2-2*1*sqrt{3}+(sqrt{3})^2})*sqrt{2}}{2}=\ frac{(sqrt {(1-sqrt{3})^2})*sqrt{2}}{2}=\ frac{(|1-sqrt{3}|)*sqrt{2}}{2}=\ frac{(sqrt{3}-1)*sqrt{2}}{2}=\ frac{sqrt{6}-sqrt{2}}{2}$