![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm:
\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)
\(=\sqrt{8-8\sqrt{3}+6}-\sqrt{18-12\sqrt{3}+6}\)
\(=\sqrt{\left(2\sqrt{2}-\sqrt{6}\right)^2}-\sqrt{\left(3\sqrt{2}-\sqrt{6}\right)^2}\)
\(=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}\)
\(=-\sqrt{2}\)
Học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
\(=2\sqrt{5}+2+\sqrt{5}-2\)
\(=3\sqrt{5}\)
b) \(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
\(=3-2\sqrt{2}+2\sqrt{2}-1\)
=2
c) \(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
\(=2-\sqrt{2}+3\sqrt{2}-2\)
\(=2\sqrt{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}=\dfrac{\sqrt{16-2.4.2\sqrt{3}+12}-\sqrt{36-2.6.2\sqrt{3}+12}}{\sqrt{2}}=\dfrac{\sqrt{\left(4-2\sqrt{3}\right)^2}-\sqrt{\left(6-2\sqrt{3}\right)^2}}{\sqrt{2}}=\dfrac{4-2\sqrt{3}-6+2\sqrt{3}}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
a.
$=2\sqrt{5}-9\sqrt{5}-2\sqrt{5}=(2-9-2)\sqrt{5}=-9\sqrt{5}$
b.
$=36\sqrt{6}-2\sqrt{6}+6\sqrt{6}=(36-2+6)\sqrt{6}=40\sqrt{6}$
![](https://rs.olm.vn/images/avt/0.png?1311)
a,\(\sqrt{\left(\sqrt{3}-1\right)^2}\) \(+\sqrt{\left(\sqrt{3}+1\right)^2}=2\sqrt{3}\)
b. \(\sqrt{\left(2\sqrt{5}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}=3\sqrt{5}\)
c,\(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}=4\)
d.\(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}=2\sqrt{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\sqrt{3}\left(2\sqrt{3}+3\sqrt{3}-\sqrt{3}\right)=\sqrt{3}\cdot4\sqrt{3}=12\)
Lời giải:
\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}=\sqrt{8+6-2\sqrt{8.6}}-\sqrt{18+6-2\sqrt{18.6}}\)
\(=\sqrt{(\sqrt{8}-\sqrt{6})^2}-\sqrt{(\sqrt{18}-\sqrt{6})^2}\)
\(=\sqrt{8}-\sqrt{6}-(\sqrt{18}-\sqrt{6})=\sqrt{8}-\sqrt{6}\)