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a)\(\sqrt{45.80}=\sqrt{9.400}=\sqrt{9}.\sqrt{400}=3.20=60\)
b) \(\sqrt{75.48}=\sqrt{25.3.16.3}=\sqrt{5^2.3^2.4^2}=5.4.3=60\)
c)\(\sqrt{90.6,4}=\sqrt{10.9.4.1,6}=\sqrt{4^2.3^2.2^2}=4.3.2=24\)
d) \(\sqrt{2,5.14,4}=\sqrt{\dfrac{25}{10}.\dfrac{144}{10}}=\sqrt{\dfrac{25.144}{100}}=\sqrt{\left(\dfrac{5.12}{10}\right)^2}=\dfrac{5.12}{10}=6\)
a) \(\sqrt{45.80}=\sqrt{9.400}=\sqrt{9}.\sqrt{400}=3.20=60\)
b)\(\sqrt{75.48}=\sqrt{25.3.3.16}=5.3.4=60\)
c)\(\sqrt{90.6,4}=\sqrt{9.64}=3.8=24\)
d)\(\sqrt{2,5.14,4}=\sqrt{\dfrac{25}{10}.\dfrac{144}{10}}=\sqrt{\dfrac{25.144}{100}=\dfrac{5.12}{10}=\dfrac{60}{10}=6}\)
a) \(\sqrt{10}.\sqrt{40}\)
=\(\sqrt{10.40}\)
=\(\sqrt{400}\)
=20
b) \(\sqrt{5.}\sqrt{45}\)
=\(\sqrt{5.45}\)
=\(\sqrt{225}\)
=\(\sqrt{15}\)
c) \(\sqrt{52.}\sqrt{13}\)
=\(\sqrt{52.13}\)
=\(\sqrt{676}\)
=26
d)\(\sqrt{2.}\sqrt{162}\)
=\(\sqrt{2.162}\)
=\(\sqrt{324}\)
=18
Bài 1 :
Câu a : \(\sqrt{\dfrac{1,44}{3,61}}=\sqrt{\dfrac{144}{361}}=\dfrac{\sqrt{144}}{\sqrt{361}}=\dfrac{12}{19}\)
Câu b : \(\sqrt{\dfrac{0,25}{9}}=\sqrt{\dfrac{25}{900}}=\dfrac{\sqrt{25}}{\sqrt{900}}=\dfrac{5}{30}=\dfrac{1}{6}\)
Câu c : \(\sqrt{1\dfrac{13}{36}}.\sqrt{3\dfrac{13}{36}}=\sqrt{\dfrac{49}{36}}.\sqrt{\dfrac{121}{46}}=\dfrac{\sqrt{49}}{\sqrt{36}}.\dfrac{\sqrt{121}}{36}=\dfrac{7}{6}.\dfrac{11}{6}=\dfrac{77}{36}\)
Câu d : \(\sqrt{\dfrac{1}{121}.3\dfrac{6}{25}}=\sqrt{\dfrac{1}{121}.\dfrac{81}{25}}=\dfrac{1}{\sqrt{121}}.\dfrac{\sqrt{81}}{\sqrt{25}}=\dfrac{1}{11}.\dfrac{9}{5}=\dfrac{9}{55}\)
Câu e : \(\sqrt{1\dfrac{13}{36}.2\dfrac{2}{49}.2\dfrac{7}{9}}=\sqrt{\dfrac{49}{36}.\dfrac{100}{49}.\dfrac{25}{9}}=\dfrac{\sqrt{49}}{\sqrt{36}}.\dfrac{\sqrt{100}}{\sqrt{49}}.\dfrac{\sqrt{25}}{\sqrt{9}}=\dfrac{7}{6}.\dfrac{10}{7}.\dfrac{5}{3}=\dfrac{25}{9}\)
Bài 2 :
Câu a : \(\dfrac{\sqrt{245}}{\sqrt{5}}=\sqrt{\dfrac{245}{5}}=\sqrt{49}=7\)
Câu b : \(\dfrac{\sqrt{3}}{\sqrt{75}}=\sqrt{\dfrac{3}{75}}=\sqrt{\dfrac{1}{25}}=\dfrac{1}{5}\)
Câu c : \(\dfrac{\sqrt{10,8}}{\sqrt{0,3}}=\sqrt{\dfrac{10,8}{0,3}}=\sqrt{\dfrac{108}{3}}=\sqrt{36}=6\)
Câu d : \(\dfrac{\sqrt{6,5}}{\sqrt{58,5}}=\sqrt{\dfrac{6,5}{58,5}}=\sqrt{\dfrac{65}{585}}=\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}\)
a,\(\sqrt{12}=2\sqrt{3}=\sqrt{3}+\sqrt{3}\)
ta có \(\sqrt{5}>\sqrt{3}\)và\(\sqrt{7}>\sqrt{3}\)=>\(\sqrt{5}+\sqrt{7}>\sqrt{12}\)
a: \(\sqrt{17}+\sqrt{26}=\dfrac{9}{\sqrt{26}-\sqrt{17}}>9\)
e: \(\sqrt{13}-\sqrt{12}=\dfrac{1}{\sqrt{13}+\sqrt{12}}\)
\(\sqrt{12}-\sqrt{11}=\dfrac{1}{\sqrt{12}+\sqrt{11}}\)
mà \(\sqrt{13}+\sqrt{12}>\sqrt{11}+\sqrt{12}\)
nên \(\sqrt{13}-\sqrt{12}< \sqrt{12}-\sqrt{11}\)
d: \(9-\sqrt{58}=\sqrt{49}-\sqrt{58}< 0< \sqrt{80}-\sqrt{59}\)
a)
\(\left(\sqrt{5}+\sqrt{7}\right)^2=12+2\sqrt{35}\)
\(\sqrt{12}^2=12\)
=>\(\sqrt{5}+\sqrt{7}>\sqrt{12}\)
các câu còn lại cũng làm như vậy
so sánh: \(4-\sqrt{2}\) và \(\sqrt{5}\)
\(\left(4-\sqrt{2}\right)^2=18-8\sqrt{2}>18-8\sqrt{2,25}=18-8.1,5=18-12=6>5=\sqrt{5}^2\Rightarrow4-\sqrt{2}>\sqrt{5}\left(vì:\left\{{}\begin{matrix}4-\sqrt{2}>0\\\sqrt{5}>0\end{matrix}\right.\right)\Rightarrow7+4-\sqrt{2}>7+\sqrt{5}\Rightarrow11-\sqrt{2}>7+\sqrt{5}\)
\(b,2006^2-2005.2007=2006^2-\left(2006-1\right)\left(2006+1\right)=2006^2-2006^2+1=1\Rightarrow2006^2>2005.2007\left(1\right)\)
\(\left(2\sqrt{2006}\right)^2=4.2006=8024;\left(\sqrt{2005}+\sqrt{2007}\right)^2=2005+2007+2\sqrt{2005.2007}=4012+2\sqrt{2005.2007}=4012+2\sqrt{2006.2006}\left(vì\left(1\right)\right)=8024=\left(2\sqrt{2006}\right)^2\)
\(\Rightarrow\sqrt{2005}+\sqrt{2007}< 2\sqrt{2006}\left(vì:\left\{{}\begin{matrix}\sqrt{2005}+\sqrt{2007}>0\\2\sqrt{2006}>0\end{matrix}\right.\right)\)
\(c,\left(\sqrt{10}+\sqrt{13}\right)^2=23+2\sqrt{130}>23+2\sqrt{121}\left(130>121\right)=23+2.11=45>4.11=\left(2\sqrt{11}\right)^2\Rightarrow\sqrt{10}+\sqrt{13}>2\sqrt{11}\left(vì\left\{{}\begin{matrix}\sqrt{10}+\sqrt{13}>0\\2\sqrt{11}>0\end{matrix}\right.\right)\)
\(d,\left(\sqrt{5}+\sqrt{7}\right)^2=12+2\sqrt{35}< 12+2\sqrt{36}=12+12=24< 15+6\sqrt{6}=\left(3+\sqrt{6}\right)^2\Rightarrow\sqrt{5}+\sqrt{7}< 3+\sqrt{6}\left(vì:\left\{{}\begin{matrix}\sqrt{5}+\sqrt{7}>0\\3+\sqrt{6}>0\end{matrix}\right.\right)\)
1. với a=2,5 thì \(\sqrt{a^2}\) =\(\left|a\right|=\)\(\left|2.5\right|=2.5\)
với a=0,3 thì \(\sqrt{a^2}\) =\(\left|a\right|=\)\(\left|0,3\right|=0,3\)
với a=-0,1 thì \(\sqrt{a^2}\) =\(\left|a\right|=\)\(\left|-0,1\right|=0,1\)
Bài 4:
a: \(=\sqrt{\dfrac{10.8}{0.3}}=\sqrt{36}=6\)
b: \(=\sqrt{\dfrac{7}{175}}=\sqrt{\dfrac{1}{25}}=\dfrac{1}{5}\)
c: \(=\sqrt{\dfrac{2.84}{0.71}}=2\)
d: \(=\sqrt{\dfrac{625}{144}}=\dfrac{25}{12}\)
\(a,\sqrt{45.8}=\sqrt{360}=\sqrt{6^2.10}=6\sqrt{10}\)
\(b,\sqrt{2,5.14,4}=\sqrt{36}=\sqrt{6^2}=6\)
\(c,\sqrt{10.40}=\sqrt{400}=\sqrt{20^2}=20\)
\(d,\sqrt{52}.\sqrt{13}=\sqrt{52.13}=\sqrt{676}=\sqrt{26^2}=26\)