Rút gọn biểu thức
1) \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8+2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
2) \(\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right):\left(\sqrt{5}-2\right)\)
3) \(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
4) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
5) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...-\frac{1}{\sqrt{98}-\sqrt{99}}+\frac{1}{\sqrt{99}-\sqrt{100}}\)
6) \(\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
7)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)
Câu 1,2,3 Ez quá rồi :3
Câu 4:
Tổng quát:
\(\frac{1}{\sqrt{a}+\sqrt{a+1}}=\frac{\sqrt{a}-\sqrt{a+1}}{a-a-1}=\sqrt{a+1}-\sqrt{a}.\) Game là dễ :v
Câu 5 ko khác câu 4 lắm :v
Câu 5:
Tổng quát:
\(\frac{1}{\sqrt{a}-\sqrt{a+1}}=\frac{\sqrt{a}+\sqrt{a+1}}{a-a-1}=-\sqrt{a}-\sqrt{a+1}.\) Game là dễ :v
Sao làm hổng ai bảo đú.n/g vậy :(((
Tính:
A) \(\left(\sqrt{3}-2\right)^2\left(\sqrt{3}-2\right)^2\)
B) \(\left(11-4\sqrt{3}\right)\left(11-4\sqrt{3}\right)\)
C) \(\left(1+\sqrt{2018}\right)\left(\sqrt{2019}-2\sqrt{2018}\right)\)
D)
\(\left(\sqrt{2}-1\right)^2+\frac{3}{2}\sqrt{\left(-2\right)}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{25}}.2\)
1. tính
a) \(\left(2\sqrt{3}+\sqrt{3}\right).\sqrt{15}+\sqrt{45}\)
b) \(\left(\sqrt{99}-3\sqrt{3}-\sqrt{11}\right).\sqrt{11}+3\sqrt{33}\)
c) \(\frac{1}{3}\sqrt{3}-\frac{1}{4}\sqrt{48}+\frac{2}{5}\sqrt{2}-\frac{1}{4}\sqrt{12}\)
d) \(\sqrt{\frac{2+\sqrt{5}}{\sqrt{5}-2}}+\sqrt{\frac{\sqrt{5}+2}{2+\sqrt{5}}}\)
help me mk đg cần gấp
a. \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
b. \(3\sqrt{\frac{9}{8}}-\sqrt{\frac{49}{2}}+\sqrt{\frac{25}{18}}\)
c. \(\left(1+\frac{5-\sqrt{5}}{1-\sqrt{5}}\right)\left(\frac{5+\sqrt{5}}{1+\sqrt{5}}+1\right)\)
d. \(\frac{2}{\sqrt{6}-2}+\frac{2}{\sqrt{6}+2}+\frac{5}{\sqrt{6}}\)
e. \(\frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}-\frac{1}{\sqrt{3}+\sqrt{2}+\sqrt{5}}\)
f. \(\frac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
CỨU TUI VỚI <3 <3
a) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
\(=\left(\sqrt{9\cdot11}-\sqrt{9\cdot2}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
\(=\left(3\sqrt{11}-3\sqrt{2}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
\(=3\cdot11-3\sqrt{22}-11+3\sqrt{22}\)
\(=33-11=22\)
b)\(3\sqrt{\frac{9}{8}}-\sqrt{\frac{49}{2}}+\sqrt{\frac{25}{18}}\)
\(=\frac{9}{\sqrt{8}}-\frac{7}{\sqrt{2}}+\frac{5}{\sqrt{18}}\)
\(=\frac{9}{2\sqrt{2}}-\frac{7}{\sqrt{2}}+\frac{5}{3\sqrt{2}}\)
\(=\frac{27-42+10}{6\sqrt{2}}\)
\(=-\frac{5}{6\sqrt{2}}\)
c)\(\left(1+\frac{5-\sqrt{5}}{1-\sqrt{5}}\right)\left(\frac{5+\sqrt{5}}{1+\sqrt{5}}+1\right)\)
\(=\left(1-\frac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}\right)\left(\frac{\sqrt{5}\left(\sqrt{5}+1\right)}{1+\sqrt{5}}+1\right)\)
\(=\left(1-\sqrt{5}\right)\left(\sqrt{5}+1\right)\)
\(=1-5=-4\)
Bài 1: Thực hiện phép tính:
a,\(\left(\frac{-3}{4}+\frac{2}{7}\right):\frac{2}{7}+\left(\frac{-1}{4}+\frac{5}{7}\right):\frac{2}{3}\)
b,\(\left(-\frac{1}{3}\right)^2\cdot\frac{4}{11}+\frac{7}{11}\cdot\left(-\frac{1}{3}\right)^2\)
c, \(\left(-\frac{1}{7}\right)^0-2\frac{4}{9}\cdot\left(\frac{2}{3}\right)^2\)
d,\(\frac{2^7\cdot9^2}{3^3\cdot2^5}\)
e,\(\left(\frac{1}{3}-\frac{5}{6}\right)^2+\frac{5}{6}:2\)
f,\(\left(9\frac{2}{4}:5,2+3.4\cdot2\frac{7}{34}\right):\left(-1\frac{9}{16}\right)\)
g,\(\sqrt{25}-3\sqrt{\frac{4}{9}}\)
h,\(\left(-2\right)^2+\sqrt{36}-\sqrt{9}+\sqrt{25}\)
i,\(\left(-\frac{1}{2}\right)^4+\left|-\frac{2}{3}\right|-2007^0\)
k,\(\left(-2\right)^3+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)
m,\(\left(-3\right)^2\cdot\frac{1}{3}-\sqrt{49}+\left(-5\right)^3:\sqrt{25}\)
n,\(\frac{\sqrt{3^2+\sqrt{39^2}}}{\sqrt{91^2}-\sqrt{\left(-7\right)^2}}\)
bài 1
a, 0,5-\(\frac{5}{41}\)+\(\frac{1}{2}-\frac{36}{41}\)
b,\(\left(-\frac{2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(\frac{-1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
c, \(\left[-\frac{3}{4}\right].\sqrt{\frac{16}{9}+3.\sqrt{49}}\)
d,\(\left(-\frac{1}{3}\right)^2.\frac{4}{11}+1\frac{5}{11}.\left(\frac{1}{3}\right)^2\)
c, \(\left(2\right)^3-\sqrt{0,36-}\left[-2,4\right]\)
Bài 1:
a) \(0,5-\frac{5}{41}+\frac{1}{2}-\frac{36}{41}\)
\(=\frac{1}{2}-\frac{5}{41}+\frac{1}{2}-\frac{36}{41}\)
\(=\left(\frac{1}{2}+\frac{1}{2}\right)-\left(\frac{5}{41}+\frac{36}{41}\right)\)
\(=1-1\)
\(=0.\)
b) \(\left(-\frac{2}{3}+\frac{3}{7}\right):\frac{4}{5}+\left(-\frac{1}{3}+\frac{4}{7}\right):\frac{4}{5}\)
\(=-\frac{2}{3}+\frac{3}{7}:\frac{4}{5}-\frac{1}{3}+\frac{4}{7}:\frac{4}{5}\)
\(=\left[\left(-\frac{2}{3}\right)-\frac{1}{3}\right]+\left(\frac{3}{7}+\frac{4}{7}\right):\frac{4}{5}\)
\(=\left(-1\right)+1:\frac{4}{5}\)
\(=\left(-1\right)+\frac{5}{4}\)
\(=\frac{1}{4}.\)
c) \(\left(-\frac{3}{4}\right).\sqrt{\frac{16}{9}+3.\sqrt{49}}\)
\(=\left(-\frac{3}{4}\right).\sqrt{\frac{16}{9}+3.7}\)
\(=\left(-\frac{3}{4}\right).\sqrt{\frac{16}{9}+21}\)
\(=\left(-\frac{3}{4}\right).\sqrt{\frac{205}{9}}\)
\(=\left(-\frac{3}{4}\right).\frac{\sqrt{205}}{3}\)
\(=-\frac{\sqrt{205}}{4}.\)
d) \(\left(-\frac{1}{3}\right)^2.\frac{4}{11}+1\frac{5}{11}.\left(\frac{1}{3}\right)^2\)
\(=\frac{1}{9}.\frac{4}{11}+\frac{16}{11}.\frac{1}{9}\)
\(=\frac{1}{9}.\left(\frac{4}{11}+\frac{16}{11}\right)\)
\(=\frac{1}{9}.\frac{20}{11}\)
\(=\frac{20}{99}.\)
Chúc bạn học tốt!
1.Chứng tỏ rằng:
A=75.(42004+42003+...+42+4+1)+25 chia hết cho 100
2.tính nhanh:
\(A=\frac{\left(1+2+3+...+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+...+99-100}\)
\(B=\frac{\left(\frac{1}{14}-\frac{\sqrt{2}}{7}+\frac{\sqrt[3]{2}}{35}\right).\left(-\frac{4}{15}\right)}{\left(\frac{1}{10}+\frac{\sqrt[3]{2}}{25}-\frac{\sqrt{2}}{5}\right).\frac{5}{7}}\)
3.a)tính giá trị của biểu thức A=3x2-2x+1 với |x|=\(\frac{1}{2}\)
b)Tìm x nguyên để \(\sqrt{x+1}\)chia hết cho \(\sqrt{x-3}\)
1. A = 75(42004 + 42003 +...+ 42 + 4 + 1) + 25
A = 25 . [3 . (42004 + 42003 +...+ 42 + 4 + 1) + 1]
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 3 + 1)
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 4)
A = 25 . 4 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1)
A =100 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1) \(⋮\) 100
3a) |x| = 1/2
=> x = 1/2 hoặc x = -1/2
với x = 1/2:
A = \(3.\left(\frac{1}{2}\right)^2-2.\frac{1}{2}+1\)
\(A=\frac{3}{4}-1+1=\frac{3}{4}\)
với x = -1/2
A = \(3.\left(-\frac{1}{2}\right)^2-2\left(-\frac{1}{2}\right)+1\)
\(A=\frac{3}{4}+1+1=\frac{3}{4}+2=\frac{11}{4}\)
2.
A=\(\frac{\left(1+2+3+.....+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+......+99-100}\)\
A=0
Thực hiện phép tính sau
a. F=[12(1)-2,3(6)]:4,(21)
b.\(\frac{1\frac{11}{34}.4\frac{3}{7}-\left(\frac{3}{2}-6\frac{1}{3}.\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}.\left(12-5\frac{1}{3}\right)}\)
c.1-\(\frac{\sqrt{121}}{\sqrt{196}}-\frac{\sqrt{169}}{\sqrt{144}}+\frac{\sqrt{25}}{\sqrt{36}}+\left(-1\frac{2}{3}\right):\left(-3\frac{1}{3}\right)\)
Minh AnNgọc HnueBăng Băng 2k6Thảo PHồ Đđề bài khó wáỖ CHÍ DŨNGBảo TrâmhLương Minh HằngươngAnh Qua
c/
\(=1-\frac{11}{14}-\frac{14}{12}+\frac{5}{6}+\frac{-5}{3}:\frac{-10}{3}\)
\(=1-\frac{11}{14}-\frac{14}{12}+\frac{5}{6}+\frac{-5}{3}.\frac{-3}{10}\)
\(=1-\frac{11}{14}-\frac{14}{12}+\frac{5}{6}+\frac{1}{2}\)
\(=1-\left(\frac{66}{84}+\frac{98}{84}-\frac{70}{84}-\frac{42}{84}\right)\)
Mik làm tiếp nhé tại lúc nãy bấm nhầm!
Câu c/ (tiếp theo)
\(=1-\frac{52}{84}\)
\(=\frac{84}{84}-\frac{52}{84}=\frac{32}{84}=\frac{8}{21}\)
Câu a: Sai đề
Rút gọn biểu thức \(B=\left(\frac{\sqrt{a-2}+2}{3}\right)\left(\frac{\sqrt{a-2}}{3+\sqrt{a-2}}+\frac{a+7}{11-a}\right):\left(\frac{3\sqrt{a-2}+1}{a-3\sqrt{a-2}-2}-\frac{1}{\sqrt{a-2}}\right)\)
