Toán 1. √8+2 √15 2. √14- 6 √5 3. √11+4 √6 4. √4-2 √3 5. √227 -30 √2 16/07/2021 By Ariana 1. √8+2 √15 2. √14- 6 √5 3. √11+4 √6 4. √4-2 √3 5. √227 -30 √2
1. $\sqrt{8+2\sqrt{15}}$ $=\sqrt{5+2\sqrt{15}+3}$ $=\sqrt{(\sqrt{5})^2+2.\sqrt{5}.\sqrt{3}+(\sqrt{3})^2}$ $=\sqrt{(\sqrt{5}+\sqrt{3})^2}$ $=\sqrt{5}+\sqrt{3}$ 2. $\sqrt{14-6\sqrt{5}}$ $=\sqrt{3^2-2.3.\sqrt{5}+5}$ $=\sqrt{(3-\sqrt{5})^2}$ 3. $\sqrt{11+4\sqrt{6}}$ $=\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}.\sqrt{3}+\left(\sqrt{3}\right)^3}$ $=\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}$ $=2.\sqrt{2}+\sqrt{3}$ 4. $\sqrt{4-2\sqrt{3}}$ $=\sqrt{(\sqrt{3}-1)^2}=\sqrt{3}-1$ 5. Mk k đọc đc đề Trả lời
1. $\sqrt{8+2\sqrt{15}}$
$=\sqrt{5+2\sqrt{15}+3}$
$=\sqrt{(\sqrt{5})^2+2.\sqrt{5}.\sqrt{3}+(\sqrt{3})^2}$
$=\sqrt{(\sqrt{5}+\sqrt{3})^2}$
$=\sqrt{5}+\sqrt{3}$
2. $\sqrt{14-6\sqrt{5}}$
$=\sqrt{3^2-2.3.\sqrt{5}+5}$
$=\sqrt{(3-\sqrt{5})^2}$
3. $\sqrt{11+4\sqrt{6}}$
$=\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}.\sqrt{3}+\left(\sqrt{3}\right)^3}$
$=\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}$
$=2.\sqrt{2}+\sqrt{3}$
4. $\sqrt{4-2\sqrt{3}}$
$=\sqrt{(\sqrt{3}-1)^2}=\sqrt{3}-1$
5. Mk k đọc đc đề
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