rút gọn biểu thức sau
3 .16 /12.9
11.5 -11.7 /11
6 /11 - 6/9 +6 /5 /21/11- 21/9+21/5
rút gọn các biểu thức
(-6).11 / (-11).(-8)
21.(-5) / 25.(-7)
32.9.11 / 12.24.22
\(\dfrac{\left(-6\right).11}{\left(-11\right).\left(-8\right)}=\dfrac{\left(-3\right).2.11}{11.2.4}=-\dfrac{3}{4}\)
\(\dfrac{21.\left(-5\right)}{25.\left(-7\right)}=\dfrac{\left(-3\right).\left(-7\right).\left(-5\right)}{\left(-5\right).\left(-5\right).\left(-7\right)}=\dfrac{3}{5}\)
\(\dfrac{32.9.11}{12.24.22}=\dfrac{4.4.2.3.3.11}{3.4.4.2.3.11.2}=\dfrac{4^2.2.3^2.11}{3^2.4^2.2^2.11}=\dfrac{1}{2}\)
\(\dfrac{\left(-6\right).11}{\left(-11\right).\left(-8\right)}\)=\(\dfrac{-3}{4}\)
\(\dfrac{21.\left(-5\right)}{25.\left(-7\right)}\)=\(\dfrac{2}{5}\)
\(\dfrac{32.9.11}{12.24.22}\)=\(\dfrac{1}{2}\)
Rút gọn biểu thức
1)\(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)
2) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)
1) \(\sqrt{6+4\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(=\sqrt{2^2+2\cdot2\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}-\sqrt{3^2-2\cdot3\cdot\sqrt{2}+\left(\sqrt{2}\right)^2}\)
\(=\sqrt{\left(2+\sqrt{2}\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\)
\(=\left|2+\sqrt{2}\right|-\left|3-\sqrt{2}\right|\)
\(=2+\sqrt{2}-3+\sqrt{2}\)
\(=2\sqrt{2}-1\)
2) \(\sqrt{21-4\sqrt{5}}+\sqrt{21+4\sqrt{5}}\)
\(=\sqrt{20-4\sqrt{5}+1}+\sqrt{20+4\sqrt{5}+1}\)
\(=\sqrt{\left(2\sqrt{5}\right)^2-2\sqrt{5}\cdot2\cdot1+1^2}+\sqrt{\left(2\sqrt{5}\right)^2+2\sqrt{5}\cdot2\cdot1-1^2}\)
\(=\sqrt{\left(2\sqrt{5}-1\right)^2}+\sqrt{\left(2\sqrt{5}+1\right)^2}\)
\(=\left|2\sqrt{5}-1\right|+\left|2\sqrt{5}+1\right|\)
\(=2\sqrt{5}-1+2\sqrt{5}+1\)
\(=4\sqrt{5}\)
Rút gọn M=\(\frac{\sqrt{21+3\sqrt{5}}+\sqrt{21-3\sqrt{5}}}{\sqrt{21}+6\sqrt{11}}+\sqrt{11-6\sqrt{2}}\)
Tính rồi rút gọn:
a) \(\dfrac{2}{9}+\dfrac{1}{9}\) b) \(\dfrac{5}{6}+\dfrac{1}{6}\) c) \(\dfrac{11}{8}-\dfrac{5}{8}\) d) \(\dfrac{5}{21}-\dfrac{2}{21}\)
Thực hiện phép tính (rút gọn biểu thức)
a)\(\left(\sqrt{3}-2\right)\sqrt{7+4\sqrt{3}}\)
b) \(\sqrt{6+\sqrt{32}}\) - \(\sqrt{11-\sqrt{72}}\)
c) \(\sqrt{21-4\sqrt{5}}\) + \(\sqrt{21+4\sqrt{5}}\)
a: \(=\left(\sqrt{3}-2\right)\cdot\sqrt{\left(2+\sqrt{3}\right)^2}\)
\(=\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)\)
=3-4=-1
b: \(=\sqrt{6+4\sqrt{2}}-\sqrt{11-2\sqrt{18}}\)
\(=\sqrt{\left(2+\sqrt{2}\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\)
\(=2+\sqrt{2}-3+\sqrt{2}=2\sqrt{2}-1\)
c: \(=\sqrt{\left(2\sqrt{5}-1\right)^2}+\sqrt{\left(2\sqrt{5}+1\right)^2}\)
\(=2\sqrt{5}-1+2\sqrt{5}+1\)
\(=4\sqrt{5}\)
Rút gọn biểu thức: P=[(1+4)(5^4+4)(9^4+4).......(21^4+4)] / [(3^4+4)(7^4+4)(11^4+4).......(23^4+4)]
câu 1: rút gọn phân số sau 63/45: A. 6/5 b. 4/5 c. 7/5 d.3/5 câu 2: phân số nào sau đây bằng phân số 4/7? A.16/28 b. 9/21 c. 6/21 D. 15/21
Rút gọn rồi tính :
a.4/16+1/4
b.15/25+6/10
c.5/9+21/27
a: =1/4+1/4=2/4=1/2
b: =3/5+3/5=6/5
c: =5/9+7/9=12/9=4/3
a, 1/4+1/4=2/4=1/4
b, 3/5+3/5=6/5
c, 5/9+7/9=12/9=4/3
a)1/4+1/4=2/4=1/4
b) 3/5+3/5=6/5
c) 5/9+7/9=12/9=4/3
rút gọn biểu thức -4/12+18/45+-6/9+6/30+-21/35