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a)<
b)>
c)<
Tìm x
a)X x 6 =3048:2
X =3048:2:6
X =254
B)56 :X =1326-1318
56 :X =8
X =56:8
X =7
\(a,4^2=16>15=\left(\sqrt{15}\right)^2\Rightarrow4>\sqrt{15}\\ b,\left(\sqrt{27}\right)^2=27>25=5^2\Rightarrow\sqrt{27}>5\\ c,6^2=36>21=\left(\sqrt{21}\right)^2\Rightarrow6>\sqrt{21}\\ d,\left(\sqrt{79}\right)^2=79< 81=9^2\Rightarrow\sqrt{79}< 9\\ e,7^2=49>47=\left(\sqrt{47}\right)^2\Rightarrow7>\sqrt{47}\\ f,\left(\sqrt{123}\right)^2=123>100=10^2\Rightarrow\sqrt{123}>10\)
a ) \(\sqrt{\frac{49}{9}-\frac{4}{3}.\sqrt{5}}=\sqrt{5-2.\sqrt{5}.\frac{2}{3}+\frac{4}{9}}=\sqrt{\left(\sqrt{5}-\frac{2}{3}\right)^2}=\sqrt{5}-\frac{2}{3}\)
b ) \(\sqrt{\frac{64}{9}-\frac{2}{3}.\sqrt{7}}=\sqrt{7-2.\sqrt{7}.\frac{1}{3}+\frac{1}{9}}=\sqrt{\left(\sqrt{7}-\frac{1}{3}\right)^2}=\sqrt{7}-\frac{1}{3}\)
c ) \(\sqrt{\frac{79}{36}+\frac{2}{3}\sqrt{7}}=\sqrt{\frac{72}{36}+2.2.\frac{\sqrt{7}}{6}+\frac{7}{36}}=\sqrt{\left(2+\frac{\sqrt{7}}{6}\right)^2}=2+\frac{\sqrt{7}}{6}=\frac{12+\sqrt{7}}{6}\)
d ) \(\sqrt{\frac{45}{4}-\sqrt{11}}=\sqrt{\frac{44}{4}-\sqrt{11}+\frac{1}{4}}=\sqrt{11-\sqrt{11}+\frac{1}{4}}=\sqrt{\left(\sqrt{11}-\frac{1}{2}\right)^2}=\sqrt{11}-\frac{1}{2}\)
a) \(9=6+3=6+\sqrt{9}\)
\(6+2\sqrt{2}=6+\sqrt{8}\)
\(\sqrt{8}< \sqrt{9}\) nên \(6+\sqrt{8}=6+2\sqrt{2}< 6+\sqrt{9}=9\)
b) \(\left(\sqrt{2}+\sqrt{3}\right)^2=5+2\sqrt{6}=5+\sqrt{24}\)
\(3^2=9=5+4=5+\sqrt{16}\)
\(\sqrt{16}< \sqrt{24}\Rightarrow3^2< \left(\sqrt{2}+\sqrt{3}\right)^2\Rightarrow3< \sqrt{2}+\sqrt{3}\)
c) \(9+4\sqrt{5}=\left(2+\sqrt{5}\right)^2\)
\(16=\left(2+2\right)^2=\left(2+\sqrt{4}\right)^2\)
\(\sqrt{4}< \sqrt{5}\Rightarrow2+\sqrt{4}< 2+\sqrt{5}\Rightarrow\left(2+\sqrt{4}\right)^2=16< \left(2+\sqrt{5}\right)^2=9+4\sqrt{5}\)
d) \(\left(\sqrt{11}-\sqrt{3}\right)^2=14-2\sqrt{33}=14-\sqrt{132}\)
\(2^2=14-10=14-\sqrt{100}\)
\(\sqrt{100}< \sqrt{132}\Leftrightarrow-\sqrt{100}>-\sqrt{132}\Leftrightarrow14-\sqrt{100}>14-\sqrt{132}\)
\(\Rightarrow2>\sqrt{11}-\sqrt{3}\)
Bài 6:
a: \(15=\sqrt{225}>\sqrt{200}\)
b: \(27=9\sqrt{9}>9\sqrt{5}\)
c: \(-24=-\sqrt{576}< -\sqrt{540}=-6\sqrt{15}\)
Đáp án là C
Ta có 9 = 81
81 < 79 ⇒ 81 < 79 hay 9 > 79