\(\sqrt{\dfrac{1}{9}}. \sqrt{0,81} .\sqrt{0,09}\)
Tính :
\(\sqrt{\dfrac{1}{9}}\) . \(\sqrt{0,81}\) + \(\sqrt{0,09}\)
\(\sqrt{\dfrac{1}{9}}\cdot\sqrt{0.81}+\sqrt{0.09}\)
=\(\dfrac{1}{3}\cdot\dfrac{3}{10}+\dfrac{3}{10}\)
=\(\dfrac{1}{10}+\dfrac{3}{10}\)
=\(\dfrac{2}{5}\)
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`
a,\(\sqrt{1}+\sqrt{9}+\sqrt{25}+\sqrt{49}+\sqrt{81}\) c\(\sqrt{0,04}+\sqrt{0,09}+\sqrt{0,16}\)
b,\(\sqrt{\dfrac{1}{4}}+\sqrt{\dfrac{1}{9}}+\sqrt{\dfrac{1}{36}}+\sqrt{\dfrac{1}{16}}\) e\(\sqrt{2^2}+\sqrt{4^2}+\sqrt{\left(-6^2\right)}+\sqrt{\left(-8^2\right)}\)
j,\(\sqrt{1,44}-\sqrt{1,69}+\sqrt{1,96}\)
g, \(\sqrt{\dfrac{4}{25}}+\sqrt{\dfrac{25}{4}}+\sqrt{\dfrac{81}{100}}+\sqrt{\dfrac{9}{16}}\)
d\(\sqrt{81}-\sqrt{64}+\sqrt{49}\)
a)\(\sqrt{1}\)+\(\sqrt{9}\)+\(\sqrt{25}\)+\(\sqrt{49}\)+\(\sqrt{81}\)
=1+3+5+7+9
=25
b)=\(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{4}\)
=\(\dfrac{6}{12}\)+\(\dfrac{4}{12}\)+\(\dfrac{2}{12}\)+\(\dfrac{3}{12}\)
=\(\dfrac{15}{12}\)
c) =0,2+0.3+0,4
= 0.9
d) =9-8+7
=8
j) =1,2-1,3+1.4
= (-0,1)+1,4
=1,4
g) \(\dfrac{2}{5}\)+\(\dfrac{5}{2}\)+\(\dfrac{9}{10}\)+\(\dfrac{3}{4}\)
= (\(\dfrac{4}{10}\)+\(\dfrac{15}{10}\)+\(\dfrac{9}{10}\))+\(\dfrac{3}{4}\)
= \(\dfrac{14}{5}\)+\(\dfrac{3}{4}\)
=\(\dfrac{56}{20}\)+\(\dfrac{15}{20}\)
= \(\dfrac{71}{20}\)
Nhớ tick cho mk nha~
\(\sqrt[]{\dfrac{\text{1}}{\text{4}}}\).\(\sqrt[]{\text{1,21}}\)-\(\sqrt[]{\text{0,09}}\)+\(\sqrt[]{\text{36}}\)
\(\sqrt{\dfrac{1}{9}.0,09.}64\)
tính hộ mk
\(=\sqrt{\dfrac{1}{9}\cdot\dfrac{9}{100}}\cdot64\\ =\sqrt{\dfrac{1}{100}}\cdot64\\ =\sqrt{\left(\dfrac{1}{10}\right)^2}\cdot64\\ =\dfrac{1}{10}\cdot64\\ =\dfrac{32}{5}\)
So sánh các số x và y, nếu
a)\(x=\sqrt{961}-\left(\frac{1}{\sqrt{6}}-1\right)\)và \(y=\sqrt{1089}-\left(\frac{1}{\sqrt{7}}+1\right)\)
b) \(\sqrt{0,01}+\sqrt{0,04}+\sqrt{0,09}+\sqrt{0,16}+...+\sqrt{0,81}\)và \(y=\sqrt{20+0,25}\)
c) \(x=\left(1-\frac{1}{\sqrt{4}}\right).\left(1-\frac{1}{\sqrt{16}}\right).\left(1-\frac{1}{\sqrt{36}}\right).\left(1-\frac{1}{\sqrt{64}}\right).\left(1-\frac{1}{\sqrt{100}}\right)\)và\(y=\sqrt{0,1}\)
Tính giá trị của biểu thức:
\(\begin{array}{l}a)\sqrt {0,49} + \sqrt {0,64} ;b)\sqrt {0,36} - \sqrt {0,81} ;\\c)8.\sqrt 9 - \sqrt {64} ;d)0,1.\sqrt {400} + 0,2.\sqrt {1600} \end{array}\)
\(\begin{array}{l}a)\sqrt {0,49} + \sqrt {0,64} = 0,7 + 0,8 = 1,5;\\b)\sqrt {0,36} - \sqrt {0,81} = 0,6 - 0,9 = - 0,3;\\c)8.\sqrt 9 - \sqrt {64} = 8.3 - 8 = 24 - 8 = 16;\\d)0,1.\sqrt {400} + 0,2.\sqrt {1600} = 0,1.20 + 0,2.40 = 2 + 8 = 10\end{array}\)
Tính
1.\(2\sqrt{4}+4\sqrt{9}+6\sqrt{25}-4\sqrt{16}+\sqrt{0}\)
2. \(2\sqrt{0,09}-7\sqrt{2,25}+8\sqrt{\frac{16}{25}}-\sqrt{1}-0\sqrt{10,1}\)
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 \(\dfrac{5}{3}+\sqrt{x+3}>0\))
\(\Leftrightarrow x-3=0\Leftrightarrow x=3\left(nhận\right)\)