Question

Упростить выражение.
1) $sqrt{7+4 sqrt{3} }$
2) $sqrt{6-2 sqrt{5} }$
3) $sqrt{5+2 sqrt{6} }$
4) $sqrt{3- sqrt{8} }$

Answer 1

1)
$sqrt{7+4sqrt{3}}=sqrt{4+2*2sqrt{3}+3}=sqrt{2^2+2*2sqrt{3}+(sqrt{3})^2}=\=sqrt{(2+sqrt{3})^2}=2+sqrt{3}$


2)
$sqrt{6-2sqrt{5}}=sqrt{5-2sqrt{5}+1}=sqrt{(sqrt{5})^2-2*1*sqrt{5}+1^2}=\=sqrt{(sqrt{5}-1)^2}=sqrt{5}-1$


3)
$sqrt{5+2sqrt{6}}=sqrt{2+2sqrt{6}+3}=sqrt{(sqrt{2})^2+2*sqrt{2}*sqrt{3}+(sqrt{3})^2}=\=sqrt{(sqrt{2}+sqrt{3})^2}=sqrt{2}+sqrt{3}$


4)
$sqrt{3-sqrt{8}}=sqrt{2-2sqrt{2}+1}=sqrt{(sqrt{2})^2-2*1*sqrt{2}+1^2}=\=sqrt{(sqrt{2}-1)^2}=sqrt{2}-1$

Answer 2

Огромнее вам спасибо!!!!!