Toán Lớp 8: $sqrt{10+sqrt{24}+sqrt{40}+sqrt{60}}$`-`$sqrt{8+2sqrt{15}}$ -

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Toán Lớp 8: $\sqrt{10+\sqrt{24}+\sqrt{40}+\sqrt{60}}$`-`$\sqrt{8+2\sqrt{15}}$

Trang Tháng Tám 2, 2022 Toán học 1 Comment 0 views

Toán Lớp 8: $\sqrt{10+\sqrt{24}+\sqrt{40}+\sqrt{60}}$-$\sqrt{8+2\sqrt{15}}$

Comments ( 1 )

thienthanh
2 Tháng Tám, 2022 at 5:28 chiều

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#tnvt

\sqrt{10+\sqrt{24}+\sqrt{40}+\sqrt{60}}-\sqrt{8+2\sqrt{15}}

=\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}-\sqrt{5+2\sqrt{5.3}+3}

=\sqrt{2+3+5+2\sqrt{2}(\sqrt{3}+\sqrt{5})+2\sqrt{15}}-\sqrt{(\sqrt{5}+\sqrt{3})^2]

=\sqrt{3+5+2\sqrt{15}+2.(\sqrt{3}+\sqrt{5}).\sqrt{2}+2}-|\sqrt{5}+\sqrt{3}|

=\sqrt{(\sqrt{3]+\sqrt{5})^2+2.(\sqrt{3}+\sqrt{5}).\sqrt{2}+\sqrt{2}^2}-\sqrt{5}-\sqrt{3}

=\sqrt{(\sqrt{3}+\sqrt{5}+\sqrt{2})^2}-\sqrt{5}-\sqrt{3}

=|\sqrt{3}+\sqrt{5]+\sqrt{2}|-\sqrt{3}-\sqrt{5]

=\sqrt{3}+\sqrt{5}+\sqrt{2}-\sqrt{3}-\sqrt{5]

=\sqrt{2}

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