Toán Lớp 9: $\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}$
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Toán Lớp 9: $\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}$
Comments ( 1 )
=sqrt{13+30sqrt{2+sqrt{9+2.2sqrt{2}.1}}}
=sqrt{13+30sqrt{2+sqrt{(2sqrt{2})^2+2.2sqrt{2}.1+1^2}}}
=sqrt{13+30sqrt{2+sqrt{(2sqrt{2}+1)^2}}}
=sqrt{13+30sqrt{2+|2sqrt{2}+1|}}
=sqrt{13+30sqrt{2+2sqrt{2}+1}}
=sqrt{13+30sqrt{3+2.sqrt{2}}
=sqrt{13+30sqrt{(sqrt{2})^2+2.sqrt{2}.1+1^2}}
=sqrt{13+30.sqrt{(sqrt{2}+1)^2}}
=sqrt{13+30.|sqrt{2}+1|}
=sqrt{13+30.(sqrt{2}+1)}
=sqrt{13+30sqrt{2}+30}
=sqrt{43+30sqrt{2}}
=sqrt{43+2.5.3sqrt{2}}
=sqrt{5^2+2.5.3sqrt{2}+(3sqrt{2})^2}
=sqrt{(5+3sqrt{2})^2}
=|5+3sqrt{2}|
=5+3sqrt{2}