Rút gọn
(2/3)^3.(-3/4)^2.(-1)^5 : (2/5)^2.(-5/12)^3
TT
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rút gọn
rút gọn biểu thức M = [ {2/7 + 2/5 + 2/17 - 2/239 _ 3/7 + 3/5 + 3/17 - 3/239 } : { 7/12 + 5/6 - 1 _ 5 - 3/4 + 1/3} ] . 27/11
chú thích :
/ : là gạch p/s nha
còn dấu _ : là tất cả trên
rút gọn biểu thức
M= {[2/7+2/5+2/17-2/239_3/7+3/5+3/17-3/239}:{7/12+5/6-1_5-3/4+1/3}]
Rút gọn :
A= ( 2 . 8^4 . 27^2 + 4 . 6^9 ) : ( 2^7 . 6^7 + 2^7 . 40 . 9^4 )
B= ( (2/3)^3 . (-3/4)^2 . (-1)^5 ) : ( ( 2/5)^2 . ( -5/12)^ 3
Rút gọn
1) (0.9)^5/(0.3)^6
2)20^5*5^410/100^5
3)4^6*9^5+6^9*120/8^4*3^12-6^11
4)4^2*25^2+32*125/2^3*5^2
1, 3^4
2, 5^405
3, -20/3
4, 4
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rút gọn (3/2 - 2/5 + 1/10) : ( 3/2 - 2/3 + 1/12)
\(\left(\dfrac{3}{2}-\dfrac{2}{5}+\dfrac{1}{10}\right):\left(\dfrac{3}{2}-\dfrac{2}{3}+\dfrac{1}{12}\right)\)
=\(\left(\dfrac{11}{10}+\dfrac{1}{10}\right):\left(\dfrac{5}{6}+\dfrac{1}{12}\right)\)
=\(\dfrac{6}{5}:\dfrac{11}{12}=\dfrac{72}{55}\)
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Rút gọn biểu thức
1) \(\sqrt{9+4\sqrt{5}}\) - \(\sqrt{9-4\sqrt{5}}\)
2) \(\sqrt{12-6\sqrt{3}}\) + \(\sqrt{12+6\sqrt{3}}\)
1) \(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
\(=\sqrt{2^2+2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}-\sqrt{2^2-2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}\)
\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)
\(=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|\)
\(=2+\sqrt{5}+2-\sqrt{5}\)
\(=4\)
2) \(\sqrt{12-6\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)
\(=\sqrt{3^2-2\cdot3\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{3^2+2\cdot3\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{\left(3+\sqrt{3}\right)^2}\)
\(=\left|3-\sqrt{3}\right|+\left|3+\sqrt{3}\right|\)
\(=3-\sqrt{3}+3+\sqrt{3}\)
\(=6\)
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Rút gọn\(a, 2^12×3^5-4^6×9^2 / 12^6+8^4×35 b, 5^10×7^3-25^5×49^2/(125×7)^3+5^9×14^3\)
Rút gọn các biểu thức sau a)√27-✓12+✓48-5✓3 b)5✓18-✓5+✓20+✓1 2 C)✓25:✓16=✓36:✓9 D)✓12+✓27-5✓3 E)2✓3-✓75+2✓12
a: \(=3\sqrt{3}-2\sqrt{3}+4\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)
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Rút gọn biểu thức sau :
2√27 - √16/3 - √48 - √8 1/3
(√125 - √12 - 2√5) (3√5 - √3 + √27)
\(2\sqrt{27}-\sqrt{\dfrac{16}{3}}-\sqrt{48}-\sqrt{8\dfrac{1}{3}}\)
\(=6\sqrt{3}-4\sqrt{\dfrac{1}{3}}-4\sqrt{3}-5\sqrt{\dfrac{1}{3}}\)
\(=2\sqrt{3}-9\sqrt{\dfrac{1}{3}}\)
\(=2\sqrt{3}-3\sqrt{9\cdot\dfrac{1}{3}}\)
\(=2\sqrt{3}-3\sqrt{3}\)
\(=-\sqrt{3}\)
________________________
\(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\)
\(=\left(5\sqrt{5}-2\sqrt{3}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+3\sqrt{3}\right)\)
\(=\left(3\sqrt{5}-2\sqrt{3}\right)\left(3\sqrt{5}+2\sqrt{3}\right)\)
\(=\left(3\sqrt{5}\right)^2-\left(2\sqrt{3}\right)^2\)
\(=15-12\)
\(=3\)
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