Question

Помогите решить (упростить выражение):
$sqrt{8- sqrt{28} } - sqrt{8+ sqrt{28} }$
$sqrt{6+ 4sqrt{2} } - sqrt{6- 4sqrt{2} }$

Answer 1

$sqrt{8-sqrt{28}}- sqrt{8+sqrt{28}} =sqrt{8-sqrt{4*7}}- sqrt{8+sqrt{4*7}} =\=sqrt{8-2sqrt{7}}- sqrt{8+2sqrt{7}} =sqrt{1+7-2sqrt{7}}- sqrt{1+7+2sqrt{7}}=\=sqrt{sqrt1^2+sqrt7^2-2sqrt{7}*sqrt1}- sqrt{sqrt1^2+sqrt7^27+2sqrt{7}*sqrt1}=\=sqrt{(sqrt1-sqrt7)^2}- sqrt{(sqrt1+sqrt7)^2}=sqrt7-sqrt1-(sqrt1+sqrt7)=\=sqrt7-sqrt1-sqrt1-sqrt7=2sqrt1=2*1=2$

$sqrt{6+4sqrt{2}}- sqrt{6-4sqrt{2}} =sqrt{4+2+2*2sqrt{2}}- sqrt{4+2-2*2sqrt{2}} =\=sqrt{2^2+sqrt2^2+2*2sqrt{2}}- sqrt{2^2+sqrt2^2-2*2sqrt{2}} =\=sqrt{(2+sqrt2)^2}- sqrt{(2-sqrt2)^2} =2+sqrt2-(2-sqrt2)=\=2+sqrt2-2+sqrt2=2sqrt2$

Answer 2

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