Question

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Answer 1

3 не поняла...............

Answer 2

$3)$

$\sqrt{5+\sqrt{24}}=\sqrt{5+\sqrt{4*6}}=\sqrt{5+2\sqrt{6}}=\sqrt{5+2\sqrt{2*3}}=$

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

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

$4)$

$\sqrt{7+\sqrt{48}}=\sqrt{7+\sqrt{4*4*3}}=\sqrt{7+2*2*\sqrt{3}}=$

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

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

$5)$

$\sqrt{17-4\sqrt{9+4\sqrt{5}}}=\sqrt{17-4\sqrt{4+5+2*2*\sqrt{5}}}=$

$=\sqrt{17-4\sqrt{2^2+2*2*\sqrt{5}+(\sqrt{5})^2}}=$

$=\sqrt{17-4\sqrt{(2+\sqrt{5})^2}}=\sqrt{17-4*(2+\sqrt{5})}=$

$=\sqrt{17-8-4\sqrt{5}}=\sqrt{9-4\sqrt{5}}=\sqrt{4+5-2*2*\sqrt{5}}=$

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

$6)$

$2\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}=2\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{4*12}}}}=$

$=2\sqrt{6+2\sqrt{5-\sqrt{12+1+2*\sqrt{12}}}}=$

$=2\sqrt{6+2\sqrt{5-\sqrt{(\sqrt{12})^2+2*\sqrt{12}+1^2}}}=$

$=2\sqrt{6+2\sqrt{5-\sqrt{(\sqrt{12}+1)^2}}}=$

$=2\sqrt{6+2\sqrt{5-(\sqrt{12}+1)}}}=$

$=2\sqrt{6+2\sqrt{4-\sqrt{12}}}=2\sqrt{6+2\sqrt{4-\sqrt{4*3}}}=$

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

$=2\sqrt{6+2\sqrt{(\sqrt{3}-1)^2}}=$

$=2\sqrt{6+2*(\sqrt{3}-1)}=2\sqrt{6+2*\sqrt{3}-2}=$

$=2\sqrt{4+2*\sqrt{3}}=2\sqrt{3+1+2*\sqrt{3}}=$

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

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