tính
a.\(\sqrt{\dfrac{289}{225}}\)
b.\(\sqrt{2\dfrac{14}{25}}\)
c.\(\sqrt{\dfrac{0,25}{9}}\)
d.\(\sqrt{\dfrac{8,1}{1,6}}\)
Tính:
a. \(\sqrt{\dfrac{289}{225}};\) b. \(\sqrt{2\dfrac{14}{25}};\) c. \(\sqrt{\dfrac{0,25}{9}};\) d. \(\sqrt{\dfrac{8,1}{1,6}}.\)
a) \(\sqrt{\dfrac{289}{225}}=\dfrac{\sqrt{289}}{\sqrt{225}}=\dfrac{17}{15}\)
b) \(\sqrt{2\dfrac{14}{25}}=\dfrac{\sqrt{64}}{\sqrt{25}}=\dfrac{8}{5}\)
c) \(\sqrt{\dfrac{0,25}{9}}=\dfrac{\sqrt{0,25}}{\sqrt{9}}=\dfrac{0,5}{3}=\dfrac{1}{6}\)
d) \(\sqrt{\dfrac{8,1}{1,6}}=\dfrac{\sqrt{81}}{\sqrt{16}}=\dfrac{9}{4}\)
Bài 28 (trang 18 SGK Toán 9 Tập 1)
Tính
a) $\sqrt{\dfrac{289}{25}}$ ; b) $\sqrt{2\dfrac{14}{25}}$ ;
c) $\sqrt{\dfrac{0,25}{9}}$ ; d) $\sqrt{\dfrac{8,1}{16}}$.
a, \(\sqrt{\frac{289}{25}}=\frac{\sqrt{289}}{\sqrt{25}}=\frac{17}{5}\)
b, \(\sqrt{2\frac{14}{25}}=\sqrt{\frac{64}{25}}=\frac{8}{5}\)
c, \(\sqrt{\frac{0,25}{9}}=\frac{\sqrt{0,25}}{\sqrt{9}}=\frac{0,5}{3}=\frac{1}{2}.\frac{1}{3}=\frac{1}{6}\)
d, \(\sqrt{\frac{8,1}{16}}\)đề có sai ko cô ?
a) căn 289 / 225 = 17/15
b) căn 64/ 25 = 8/5
c) căn 0,25 / 9 = 1/6
d) căn 8,1 / 1,6 = 9/4
Câu 1 : -\(\sqrt{9}+\sqrt{0,25=}\)
A. 3,5 B.-3,5 C.2,5 D-2,5
Câu 2 :\(\sqrt{\dfrac{9}{6}-\sqrt{ }6^2}=\)
A-\(\dfrac{21}{4}\) B\(\dfrac{21}{4}\) C-\(\dfrac{27}{4}\) D\(\dfrac{27}{4}\)
Câu 3 : 2,5 . x - 3,35 = -10 nên:
A.x=2,65 B.x= -2,66 C.x=2,67 D.x= 2,68
Câu 4 :Mai và Lan cùng nhau làm mứt dừa theo công thức cứ 2 kg vừa thì cần 3 kg đường . Hỏi hai bạn làm mứt từ 2,5 kg dừa thì cần bao nhiêu kg đường?
A .3,5 B.3,6 C.3,75 D.3,8
Câu 5 :Nếu x và y là hai đại lượng tỉ lệ nghịch và x=4, y=42 thì hệ số tỉ lệ của y đối với x là:
A.168 B.178 C.169 D.160
Câu 6 : Hàm số y = f(x) = 4 . x -\(\dfrac{4}{3}\). Tính f (\(\dfrac{1}{3}\)) là :
A.\(\dfrac{1}{3}\) B.0 C.\(\dfrac{4}{3}\) D.\(\dfrac{5}{3}\)
Câu 7 : Cho hàm số y = f(x) = x\(^2\) - 5 . Khi đó :
A.f(1)=4 B.f(-2) = -9 C.f(1) >f(-1) D.f(2)= f(-2)
Mn giúp em với ^^
giúp mình với
1, tính
a, \(7\times\sqrt{\dfrac{6^2}{7^2}}-\sqrt{25}+\sqrt{\dfrac{\left(-3\right)^2}{2}}\)
b, \(-\sqrt{\dfrac{64}{49}}-\dfrac{3}{5}\times\sqrt{\dfrac{25}{64}}+\sqrt{0,25}\)
c, \(\sqrt{\dfrac{10000}{5}}-\dfrac{1}{4}.\sqrt{\dfrac{16}{9}}+\sqrt{\dfrac{\left(-3\right)^2}{\left(4\right)}}\)
d, \(\left|\dfrac{1}{4}-\sqrt{0,0144}\right|-\dfrac{3}{2}+\sqrt{\dfrac{81}{169}}\)
a: \(=7\cdot\dfrac{6}{7}-5+\dfrac{3\sqrt{2}}{2}=1+\dfrac{3}{2}\sqrt{2}\)
b: \(=-\dfrac{8}{7}-\dfrac{3}{5}\cdot\dfrac{5}{8}+\dfrac{1}{2}=\dfrac{-16+7}{14}-\dfrac{3}{8}=\dfrac{-9}{14}-\dfrac{3}{8}\)
\(=\dfrac{-72-42}{112}=\dfrac{-114}{112}=-\dfrac{57}{56}\)
c: \(=20\sqrt{5}-\dfrac{1}{4}\cdot\dfrac{4}{3}+\dfrac{3}{2}=20\sqrt{5}+\dfrac{3}{2}-\dfrac{1}{3}=20\sqrt{5}+\dfrac{7}{6}\)
a) \(\sqrt{4x^2-9}=2\sqrt{x+3}\)
b) \(\sqrt{4x+20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
c) \(\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27\sqrt{\dfrac{x-1}{81}}=4\)
d)\(5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)
\(a) \sqrt{4x^2− 9} = 2\sqrt{x + 3}\)
\(ĐK:x\ge\dfrac{3}{2}\)
\(pt\Leftrightarrow4x^2-9=4\left(x+3\right)\)
\(\Leftrightarrow4x^2-9=4x+12\)
\(\Leftrightarrow4x^2-4x-21=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1-\sqrt{22}}{2}\left(l\right)\\x=\dfrac{1+\sqrt{22}}{2}\left(tm\right)\end{matrix}\right.\)
\(b)\sqrt{4x-20}+3.\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
\(ĐK:x\ge5\)
\(pt\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)
\(\Leftrightarrow2\sqrt{x-5}=4\Leftrightarrow\sqrt{x-5}=2\)
\(\Leftrightarrow x-5=4\Leftrightarrow x=9\left(tm\right)\)
\(c)\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27.\sqrt{\dfrac{x-1}{81}}=4\)
ĐK:x>=1
\(pt\Leftrightarrow2\sqrt{x-1}-\sqrt{x-1}+3\sqrt{x-1}=4\)
\(\Leftrightarrow4\sqrt{x-1}=4\Leftrightarrow\sqrt{x-1}=1\)
\(\Leftrightarrow x-1=1\Leftrightarrow x=2\left(tm\right)\)
\(d)5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)
\(ĐK:x\ge3\)
\(pt\Leftrightarrow3\sqrt{x-3}-\dfrac{14}{3}\sqrt{x-3}-7\sqrt{x^2-9}+6\sqrt{x^2-9}=0\)
\(\Leftrightarrow-\dfrac{5}{3}\sqrt{x-3}-\sqrt{x^2-9}=0\Leftrightarrow\dfrac{5}{3}\sqrt{x-3}+\sqrt{x^2-9}=0\)
\(\Leftrightarrow(\dfrac{5}{3}+\sqrt{x+3})\sqrt{x-3}=0\)
\(\Leftrightarrow\sqrt{x-3}=0\) (vì \(\dfrac{5}{3}+\sqrt{x+3}>0\))
\(\Leftrightarrow x-3=0\Leftrightarrow x=3\left(nhận\right)\)
1) thực hiện phép tính
a) \(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
b) \(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)
c) \(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}\)
giúp mk vs ạ mk đang cần gấp
a)\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
\(=2.\sqrt{\dfrac{4^2}{3}}-3.\sqrt{\dfrac{1}{3.3^2}}-6\sqrt{\dfrac{2^2}{3.5^2}}\)
\(=2.\dfrac{4}{\sqrt{3}}-3.\dfrac{1}{3\sqrt{3}}-6.\dfrac{2}{5\sqrt{3}}=\dfrac{8}{\sqrt{3}}-\dfrac{1}{\sqrt{3}}-\dfrac{12}{5\sqrt{3}}\)\(=\dfrac{23}{5\sqrt{3}}=\dfrac{23\sqrt{3}}{15}\)
b)\(\left(6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}\right).\sqrt{\dfrac{1}{2}}\)
\(=6\sqrt{\dfrac{8}{9}.\dfrac{1}{2}}-5\sqrt{\dfrac{32}{25}.\dfrac{1}{2}}+14\sqrt{\dfrac{18}{49}.\dfrac{1}{2}}\)
\(=6\sqrt{\dfrac{4}{9}}-5\sqrt{\dfrac{16}{25}}+14\sqrt{\dfrac{9}{49}}\)\(=6.\dfrac{2}{3}-5.\dfrac{4}{5}+14.\dfrac{3}{7}=6\)
c)\(\sqrt{\left(\sqrt{2}-2\right)^2}-\sqrt{6+4\sqrt{2}}=\left|\sqrt{2}-2\right|-\sqrt{4+2.2\sqrt{2}+2}=2-\sqrt{2}-\sqrt{\left(2+\sqrt{2}\right)^2}\)
\(=2-\sqrt{2}-\left(2+\sqrt{2}\right)=-2\sqrt{2}\)
giúp mình với
1, tính
a, \(7\times\sqrt{\dfrac{6^2}{7^2}}-\sqrt{25}+\sqrt{\dfrac{\left(-3\right)^2}{2}}\)
b, \(-\sqrt{\dfrac{64}{49}}-\dfrac{3}{5}\times\sqrt{\dfrac{25}{64}}+\sqrt{0,25}\)
c, \(\sqrt{\dfrac{10000}{5}}-\dfrac{1}{4}.\sqrt{\dfrac{16}{9}}+\sqrt{\dfrac{\left(-3\right)^2}{\left(4\right)}}\)
d, \(\left|\dfrac{1}{4}-\sqrt{0,0144}\right|-\dfrac{3}{2}+\sqrt{\dfrac{81}{169}}\)
1. tính
a,\(\sqrt{\dfrac{1,44}{3,61}}\) ; b, \(\sqrt{\dfrac{0,25}{9}}\) ; c, \(\sqrt{1\dfrac{13}{36}}.\sqrt{3\dfrac{13}{36}}\)
d,\(\sqrt{\dfrac{1}{121}.3\dfrac{6}{25}}\) ; e,\(\sqrt{1\dfrac{13}{36}.2\dfrac{2}{49}.2\dfrac{7}{9}}\) ; g,
2. Tính
a, \(\dfrac{\sqrt{245}}{\sqrt{5}}\) ; b, \(\dfrac{\sqrt{3}}{\sqrt{75}}\) ; c, \(\dfrac{\sqrt{10,8}}{\sqrt{0,3}}\) ; d, \(\dfrac{\sqrt{6,5}}{\sqrt{58,5}}\)
3. Tính.
a, \(\sqrt{\dfrac{61^2-60^2}{81}}\) ; b, \(\sqrt{\dfrac{74^2-24^2}{121}}\)
4. Tìm số x không âm, biết:
a, 9 - 4 \(\sqrt{x}=1\) ; b, \(\sqrt{\dfrac{x}{5}}=4\) c, \(\sqrt{7x}< 9\)
Bài 1 :
Câu a : \(\sqrt{\dfrac{1,44}{3,61}}=\sqrt{\dfrac{144}{361}}=\dfrac{\sqrt{144}}{\sqrt{361}}=\dfrac{12}{19}\)
Câu b : \(\sqrt{\dfrac{0,25}{9}}=\sqrt{\dfrac{25}{900}}=\dfrac{\sqrt{25}}{\sqrt{900}}=\dfrac{5}{30}=\dfrac{1}{6}\)
Câu c : \(\sqrt{1\dfrac{13}{36}}.\sqrt{3\dfrac{13}{36}}=\sqrt{\dfrac{49}{36}}.\sqrt{\dfrac{121}{46}}=\dfrac{\sqrt{49}}{\sqrt{36}}.\dfrac{\sqrt{121}}{36}=\dfrac{7}{6}.\dfrac{11}{6}=\dfrac{77}{36}\)
Câu d : \(\sqrt{\dfrac{1}{121}.3\dfrac{6}{25}}=\sqrt{\dfrac{1}{121}.\dfrac{81}{25}}=\dfrac{1}{\sqrt{121}}.\dfrac{\sqrt{81}}{\sqrt{25}}=\dfrac{1}{11}.\dfrac{9}{5}=\dfrac{9}{55}\)
Câu e : \(\sqrt{1\dfrac{13}{36}.2\dfrac{2}{49}.2\dfrac{7}{9}}=\sqrt{\dfrac{49}{36}.\dfrac{100}{49}.\dfrac{25}{9}}=\dfrac{\sqrt{49}}{\sqrt{36}}.\dfrac{\sqrt{100}}{\sqrt{49}}.\dfrac{\sqrt{25}}{\sqrt{9}}=\dfrac{7}{6}.\dfrac{10}{7}.\dfrac{5}{3}=\dfrac{25}{9}\)
Bài 2 :
Câu a : \(\dfrac{\sqrt{245}}{\sqrt{5}}=\sqrt{\dfrac{245}{5}}=\sqrt{49}=7\)
Câu b : \(\dfrac{\sqrt{3}}{\sqrt{75}}=\sqrt{\dfrac{3}{75}}=\sqrt{\dfrac{1}{25}}=\dfrac{1}{5}\)
Câu c : \(\dfrac{\sqrt{10,8}}{\sqrt{0,3}}=\sqrt{\dfrac{10,8}{0,3}}=\sqrt{\dfrac{108}{3}}=\sqrt{36}=6\)
Câu d : \(\dfrac{\sqrt{6,5}}{\sqrt{58,5}}=\sqrt{\dfrac{6,5}{58,5}}=\sqrt{\dfrac{65}{585}}=\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}\)
Bài 3 :
Câu a : \(\sqrt{\dfrac{61^2-60^2}{81}}=\sqrt{\dfrac{\left(61-60\right)\left(61+60\right)}{81}}=\sqrt{\dfrac{121}{81}}=\dfrac{\sqrt{121}}{81}=\dfrac{11}{9}\)
Câu b : \(\sqrt{\dfrac{74^2-24^2}{121}}=\sqrt{\dfrac{\left(74+24\right)\left(74-24\right)}{121}}=\sqrt{\dfrac{98.50}{121}}=\dfrac{\sqrt{4900}}{\sqrt{121}}=\dfrac{70}{11}\)
Bài 4 :
Câu a : \(9-4\sqrt{x}=1\Leftrightarrow4\sqrt{x}=8\Leftrightarrow\sqrt{x}=2\Leftrightarrow x=4\)
Câu b : \(\sqrt{\dfrac{x}{5}}=4\Leftrightarrow\dfrac{x}{5}=16\Leftrightarrow x=80\)
Câu c : \(\sqrt{7x}< 9\Leftrightarrow7x< 81\Leftrightarrow x< \dfrac{81}{7}\)
a) \(\dfrac{2}{5}\sqrt{25}\) -\(\dfrac{1}{2}\sqrt{4}\) b)0,5\(\sqrt{0,09}\) +5\(\sqrt{0,81}\) c)\(\dfrac{2}{5}\sqrt{\dfrac{25}{36}}\) -\(\dfrac{5}{2}\sqrt{\dfrac{4}{25}}\)
d)-2\(\sqrt{\dfrac{-36}{-16}}\) + 5\(\sqrt{\dfrac{-81}{-25}}\)
`#3107.101107`
a)
`2/5 \sqrt{25} - 1/2 \sqrt{4}`
`= 2/5 * \sqrt{5^2} - 1/2 * \sqrt{2^2}`
`= 2/5*5 - 1/2*2`
`= 2 - 1`
`= 1`
b)
`0,5*\sqrt{0,09} + 5*\sqrt{0,81}`
`= 0,5*\sqrt{(0,3)^2} + 5*\sqrt{(0,9)^2}`
`= 0,5*0,3 + 5*0,9`
`= 0,15 + 4,5`
`= 4,65`
c)
`2/5\sqrt{25/36} - 5/2\sqrt{4/25}`
`= 2/5*\sqrt{(5^2)/(6^2)} - 5/2*\sqrt{(2^2)/(5^2)}`
`= 2/5*5/6 - 5/2*2/5`
`= 1/3 - 1`
`= -2/3`
d)
`-2 \sqrt{(-36)/(-16)} + 5 \sqrt{(-81)/(-25)}`
`= -2*\sqrt{36/16} + 5*\sqrt{81/25}`
`= -2*\sqrt{(6^2)/(4^2)} + 5*\sqrt{(9^2)/(5^2)}`
`= -2*6/4 + 5*9/5`
`= -3 + 9`
`= 6`