Thực hiện các phép tính:
a)[ 2,11/25-0,84.(6&8/9:2&7/12-5/12*4&4/35)] : [7,605:7&1/2+3,086]
b)4&3/4+(-0,37)+1/8+(1,28)+(-2,5)+3&1/2
c) 3/5*7+3/7*9+3/9*11+...+3/61*63
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\(\dfrac{3}{5}+\dfrac{13}{25}-\dfrac{5}{9}-\dfrac{3}{7}\)
\(=\dfrac{15}{25}+\dfrac{13}{25}-\dfrac{35}{63}-\dfrac{27}{63}\)
\(=\dfrac{28}{25}-\dfrac{62}{63}=\dfrac{214}{1575}\)
a: \(=4\cdot2\sqrt{6}-3\cdot3\sqrt{6}+5\sqrt{6}-5\sqrt{6}\)
\(=8\sqrt{6}-9\sqrt{6}=-\sqrt{6}\)
b: \(=2\left(3-2\sqrt{2}\right)-2\left(3+2\sqrt{2}\right)\)
\(=6-4\sqrt{2}-6-4\sqrt{2}=-8\sqrt{2}\)
c: \(=\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
\(=\dfrac{\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}=-\dfrac{2}{\sqrt{2}}=-\sqrt{2}\)
a: Ta có: \(\left(8\cdot5^7+5^6-5^5\right):5^5\)
\(=8\cdot5^2+5-1\)
\(=200+4=204\)
b: Ta có: \(\left(9^{30}-27^{19}\right):3^{57}+\left(125^9-25^{12}\right):5^{24}\)
\(=3^{60}:3^{57}-3^{57}:3^{57}+5^{27}:5^{24}-5^{24}:5^{24}\)
\(=27-1+125-1\)
=150
a. (8,57 - 55 + 56) : 55
= (8,57 : 55) - (55 : 55) + (56 : 55)
= 1,72 - 1 + 5
= 2,89 - 1 + 5
= 6,89
b. (930 - 2719) : 357 + (1259 - 2512) : 524
= (930 : 357) - (2719 : 357) + (1259 : 524) - (2512 : 524)
= 33 - 1 + 125 - 1
= 27 - 1 + 125 - 1
= 150
c. (1012 + 511 . 29 - 513 - 28) : 4 . 55 . 106
= (1012 + 2,5 , 1010 - 513 - 28) : 1,25 . 1010
= (1012 : 1,25 . 1010) + (2,5 . 1010 : 1,25 . 1010) - (513 : 1,25 . 1010) - (28 : 1,25 . 1010)
= 80 + 2 - \(\dfrac{25}{256}\) - \(\dfrac{1}{48828125}\)
= 81,90234373 \(\approx\) 82
\(a,=2xy^3\\ b,=xy+3xy^2-4\\ c,=\left(x-4\right)\left(x+4\right):\left(x-4\right)=x+4\\ d,=\left(x+5\right)^2:\left(x+5\right)=x+5\)
a) \(\sqrt{25-9}\) = \(\sqrt{16}\) = 4
b) \(\sqrt{0,01}-\sqrt{0,25}\) = 0,1 - 0,5 = -0,4
c)\(\sqrt{2.2^2+4^2}+5^2\) = \(\sqrt{2.4+16+25}\) = \(\sqrt{8+16+25}\) = \(\sqrt{49}\) = 7