(√63-2√28+3√7).√7
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70 : 7 = 10
28 : 7 =4
30 : 6 = 5
8 : 2 = 9
63 : 7 = 9
42 : 6 = 7
35 : 5 = 6
27 : 3 = 9
14 : 7 = 2
42 : 7 = 6
35 : 7 = 5
56 : 7 = 8.
\(\sqrt{28}-\sqrt{63}+\dfrac{7+\sqrt{7}}{\sqrt{7}}-\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(=\sqrt{4.7}-\sqrt{9.7}+\dfrac{\sqrt{7}\left(\sqrt{7}+1\right)}{\sqrt{7}}-\left|\sqrt{7}+1\right|\)
\(=2\sqrt{7}-3\sqrt{7}+\left(\sqrt{7}+1\right)-\left(\sqrt{7}+1\right)=-\sqrt{7}\)
Ta có: \(\left(2\sqrt{112}+5\sqrt{7}+2\sqrt{63}-2\sqrt{28}\right)\cdot\sqrt{7}\)
\(=\left(8\sqrt{7}+5\sqrt{7}+6\sqrt{7}-4\sqrt{7}\right)\cdot\sqrt{7}\)
\(=15\sqrt{7}\cdot\sqrt{7}\)
=105
a) 7 x 5 = 35 7 x 6 = 42 7 x 8 = 56 7 x 4 = 28
35 : 7 = 5 42 : 7 = 6 56 : 7 = 8 28 : 7 = 4
b) 42 : 7 = 6 35 : 7 = 5 63 : 7 = 9 16 : 2 = 8
14 : 7 = 2 49 : 7 = 7 7 : 7 = 1 48 : 6 = 8
28 : 7 = 4 70 : =10 21 : 7 = 3 56 : 7 = 8
1: \(\sqrt{147}+\sqrt{54}-4\sqrt{27}\)
\(=7\cdot\sqrt3+3\sqrt6-4\cdot3\sqrt3\)
\(=3\sqrt6+7\sqrt3-12\sqrt3=3\sqrt6-5\sqrt3\)
2: \(\sqrt{28}-4\cdot\sqrt{63}+7\cdot\sqrt{112}\)
\(=2\sqrt7-4\cdot3\sqrt7+7\cdot4\sqrt7\)
\(=2\sqrt7-12\sqrt7+28\sqrt7=18\sqrt7\)
3: \(\sqrt{49}-5\cdot\sqrt{28}+\frac12\cdot\sqrt{63}\)
\(=7-5\cdot2\sqrt7+\frac12\cdot3\sqrt7=7-10\sqrt7+1,5\sqrt7=7-8,5\cdot\sqrt7\)
4: \(\left(2\sqrt6-4\sqrt3-\frac14\sqrt8\right)\cdot3\sqrt6\)
\(=6\cdot\sqrt{36}-12\sqrt{18}-\frac14\cdot2\cdot\sqrt2\cdot3\sqrt6\)
\(=36-36\sqrt2-\frac32\sqrt{12}=36-36\sqrt2-3\sqrt3\)
6: \(\left(\sqrt{48}-3\sqrt{27}-\sqrt{147}\right):\sqrt3=\sqrt{\frac{48}{3}}-3\cdot\sqrt{\frac{27}{3}}-\sqrt{\frac{147}{3}}\)
\(=\sqrt{16}-3\cdot\sqrt9-\sqrt{49}=4-3\cdot3-7\)
=-3-9
=-12
5: \(\left(2\cdot\sqrt{1\frac{9}{16}}-5\cdot\sqrt{5\frac{1}{16}}\right):\sqrt{16}\)
\(=\left(2\cdot\sqrt{\frac{25}{16}}-5\cdot\sqrt{\frac{81}{16}}\right):\sqrt{16}\)
\(=\left(2\cdot\frac54-5\cdot\frac94\right):4=\frac{10-45}{4\cdot4}=\frac{-35}{16}\)
7: \(\left(\sqrt{50}-3\sqrt{49}\right):\sqrt2-\sqrt{162}:\sqrt2\)
\(=\left(5\sqrt2-21\right):\sqrt2-9\sqrt2:\sqrt2\)
\(=5-\frac{21}{\sqrt2}-9=-4-\frac{21\sqrt2}{2}=\frac{-8-21\sqrt2}{2}\)
8: \(\left(2\cdot\sqrt{1\frac{9}{10}}-\sqrt{5\frac{1}{10}}\right):\sqrt{10}=\left(2\cdot\sqrt{\frac{19}{10}}-\sqrt{\frac{51}{10}}:\sqrt{10}\right)\)
\(=2\cdot\frac{\sqrt{19}}{10}-\frac{\sqrt{51}}{10}=\frac{2\sqrt{19}-\sqrt{51}}{10}\)
9: \(2\cdot\sqrt{\frac{16}{3}}-3\cdot\sqrt{\frac{1}{27}}-6\cdot\sqrt{\frac{4}{75}}\)
\(=2\cdot\frac{4}{\sqrt3}-3\cdot\frac{1}{3\sqrt3}-6\cdot\frac{2}{5\sqrt3}\)
\(=\frac{8}{\sqrt3}-\frac{1}{\sqrt3}-\frac{12}{5\sqrt3}=\frac{7}{\sqrt3}-\frac{12}{5\sqrt3}=\frac{7\sqrt3}{3}-\frac{12\sqrt3}{15}=\frac{35\sqrt3-12\sqrt3}{15}=\frac{23\sqrt3}{15}\)
10: \(2\sqrt{27}-6\cdot\sqrt{\frac43}+\frac35\cdot\sqrt{75}\)
\(=2\cdot3\sqrt3-6\cdot\frac{2}{\sqrt3}+\frac35\cdot5\sqrt3\)
\(=6\sqrt3-4\sqrt3+3\sqrt3=5\sqrt3\)
11: \(\frac{\sqrt{18}}{\sqrt2}-\frac{\sqrt{12}}{\sqrt3}=\sqrt9-\sqrt4=3-2=1\)
\(\left(\sqrt{63}-2\sqrt{28}+3\sqrt{7}\right)\cdot\sqrt{7}\\ =\left(\sqrt{9\cdot7}-2\sqrt{4\cdot7}+3\sqrt{7}\right)\cdot\sqrt{7}\\ =\left(3\sqrt{7}-4\sqrt{7}+3\sqrt{7}\right)\cdot\sqrt{7}\\ =3\cdot7-4\cdot7+3\cdot7\\ =21-28+21\\ =14\)
ấn chữ M ngược cho dễ hiểu