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a) \(\sqrt{4}+\sqrt{4}\)
\(=2+2\)
\(=4\)
b) \(\sqrt{9+9+9+9+9.5}+\sqrt{81}\)
\(=9+9\)
\(=18\)
c) \(\sqrt{15}+\sqrt{15}=2\sqrt{15}\)
a) \(\sqrt{4}\)+ \(\sqrt{4}\)= 2 + 2 = 4
b) \(\sqrt{9+9+9+9+9.5}\)+ \(\sqrt{81}\)= \(\sqrt{81}\)+\(\sqrt{81}\)= 9 + 9 = 18
c) \(\sqrt{15}\)+\(\sqrt{15}\)= 7,745966692
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\left(\dfrac{3}{2}-3\right).\sqrt{\dfrac{25}{16}}=\left(-\dfrac{3}{2}\right).\dfrac{5}{4}=-\dfrac{15}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1,5.\sqrt{\dfrac{4}{9}}-\sqrt{\dfrac{9}{25}}=\dfrac{3}{2}.\dfrac{2}{3}-\dfrac{3}{5}=1-\dfrac{3}{5}=\dfrac{2}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{16}-\sqrt{9}+\sqrt{16+9}-\sqrt{\left(-2\right)^2}\)
\(=4-3+5-2=4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1.
a. \(0,5\sqrt{100}-\sqrt{\dfrac{4}{25}}=5-\dfrac{2}{5}=\dfrac{23}{5}>1\)
\(\dfrac{\left(\sqrt{1\dfrac{1}{9}}-\sqrt{\dfrac{9}{16}}\right)}{5}=\dfrac{\dfrac{\sqrt{10}}{3}-\dfrac{3}{4}}{5}=\dfrac{-9+4\sqrt{10}}{60}\approx0,06< 1\)
\(\Rightarrow0,5\sqrt{100}-\sqrt{\dfrac{4}{25}}>\dfrac{\left(\sqrt{1\dfrac{1}{9}}-\sqrt{\dfrac{9}{16}}\right)}{5}\)
2.
Ta có:
\(\left(\sqrt{a+b}\right)^2=a+b\)
\(\left(\sqrt{a}+\sqrt{b}\right)=\left(\sqrt{a}\right)^2+2\sqrt{ab}+\left(\sqrt{b}\right)^2=a+2\sqrt{ab}+b\)
=> \(\sqrt{a+b}< \sqrt{a}+\sqrt{b}\)
1b.
Áp dụng công thức trên
=> \(\sqrt{25+9}< \sqrt{25}+\sqrt{9}\)
2.
\(\sqrt{a+b}< \sqrt{a}+\sqrt{b}\\ \Rightarrow a+b< a+2\sqrt{ab}+b\\ \Rightarrow2\sqrt{ab}>0\\ \Rightarrow\sqrt{ab}>0\)
Luôn đúng với mọi a;b dươn g
=> đpcm
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\sqrt{64}-\sqrt{16}+\sqrt{\left(-5\right)^2}\)
\(=8+4+5\)
\(=17\)
\(b,\sqrt{49}+\sqrt{4}-\sqrt{9}.\sqrt{144}\)
\(=7+2-3.12\)
\(=9-36\)
\(=-27\)
7x7=49
= 14
nho ket ben voi minh nhe