Tính giá trị biểu thức sau bằng 2 cách:
A= (\(\sqrt{2}-\sqrt{3}\))\(\sqrt{10+4\sqrt{6}}\)
Tính giá trị biểu thức sau bằng 2 cách:
A= (\(\sqrt{2}-\sqrt{3}\))\(\sqrt{10+4\sqrt{6}}\)
\(=\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{6}+2\right)\)
\(=2\sqrt{3}+2\sqrt{2}-3\sqrt{2}-2\sqrt{3}=-\sqrt{2}\)
Rút gọn biểu thức: 12.(√5/6-√6/5)
\(=12\cdot\sqrt{\dfrac{5}{6}}-12\cdot\sqrt{\dfrac{6}{5}}\)
\(=2\sqrt{30}-\dfrac{12}{5}\sqrt{30}=-\dfrac{2}{5}\sqrt{30}\)
Tìm giá trị nhỏ nhất của \(A=\dfrac{x-10}{\sqrt{x-1}-3}\).
Cảm ơn mọi người ạ!
\(A=\dfrac{x-1-9}{\sqrt{x-1}-3}=\dfrac{\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+3\right)}{\sqrt{x-1}-3}\)
\(=\sqrt{x-1}+3>=3\)
Dấu '=' xảy ra khi x=1
a: \(=-xy\cdot\dfrac{\sqrt{y}}{\sqrt{x}}=-\sqrt{x}\cdot y\sqrt{y}\)
b: \(=\sqrt{\dfrac{-105x^3}{35\cdot35}}=\dfrac{\sqrt{-105x^3}}{35}\)
c: \(=\sqrt{5a}\cdot\dfrac{a}{7\sqrt{b}}\)
d: \(=-7\sqrt{3}\sqrt{xy}\)
6\(\sqrt{12}\)-\(\sqrt{20}\)-2\(\sqrt{27}\)+\(\sqrt{125}\)-6\(\sqrt{3}\)
4\(\sqrt{18}\)+2\(\sqrt{2}\)-5\(\sqrt{8}\)+\(\sqrt{32}\)
5\(\sqrt{12}\)-4\(\sqrt{3}\)+\(\sqrt{48}\)-2\(\sqrt{75}\)
`a, = 12 sqrt 3 - 2 sqrt 5 - 6 sqrt 3 + 5 sqrt 5 - 6 sqrt 3`
`= 3 sqrt 5`
`b, = 12 sqrt 2 + 2 sqrt 2 - 10 sqrt 2 + 4 sqrt 2`
`= 8 sqrt 2`
`c, = 10 sqrt 3 - 4 sqrt 3 + 4sqrt 3 - 10 sqrt 5`
`= 10(sqrt 3 - sqrt 5)`.
\(\left(\dfrac{\sqrt{216}}{3}-\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(\dfrac{6\sqrt{6}}{3}-\dfrac{\left(2\sqrt{3}-\sqrt{6}\right)\left(\sqrt{8}+2\right)}{\left(\sqrt{8}-2\right)\left(\sqrt{8}+2\right)}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(2\sqrt{6}-\dfrac{4\sqrt{6}+4\sqrt{3}-4\sqrt{3}-2\sqrt{6}}{4}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(2\sqrt{6}-\dfrac{2\sqrt{6}}{4}\right).\dfrac{1}{\sqrt{6}}.\\ =\left(2\sqrt{6}-\dfrac{\sqrt{6}}{2}\right).\dfrac{1}{\sqrt{6}}.\\ =2\sqrt{6}.\dfrac{1}{\sqrt{6}}-\dfrac{\sqrt{6}}{2}.\dfrac{1}{\sqrt{6}}.\\ =2-\dfrac{1}{2}=\dfrac{3}{2}.\)
\(=\left(\sqrt{5}-1-5\right)\left(\sqrt{5}+6\right)\)
\(=\left(\sqrt{5}-6\right)\left(\sqrt{5}+6\right)\)
=5-121=-116
rút gọn biểu thức
a) \(\sqrt{75}\)+ \(\sqrt{48}\)- \(\sqrt{300}\)
b) \(\sqrt{98}\)- \(\sqrt{72}\)+0,5\(\sqrt{8}\)
c) \(\sqrt{99}\)-\(\sqrt{11}\)+2\(\sqrt{44}\)
Lời giải:
a.
$\sqrt{75}+\sqrt{48}-\sqrt{300}=5\sqrt{3}+4\sqrt{3}-10\sqrt{3}=(5+4-10)\sqrt{3}=-\sqrt{3}$
b.
$\sqrt{98}-\sqrt{72}+0,5\sqrt{8}=7\sqrt{2}-6\sqrt{2}+\sqrt{2}=(7-6+1)\sqrt{2}=2\sqrt{2}$
c.
$\sqrt{99}-\sqrt{11}+2\sqrt{44}=3\sqrt{11}-\sqrt{11}+4\sqrt{11}$
$=(3-1+4)\sqrt{11}=6\sqrt{11}$
\(a\sqrt{75}+\sqrt{48}-\sqrt{300}\)
=\(5\sqrt{3}+4\sqrt{3}-10\sqrt{3}\)
=\(\left(4+5-10\right)\sqrt{3}\)
=-\(\sqrt{3}\)
b\(\sqrt{95}-\sqrt{72}+0,5\sqrt{8}\)
=\(\sqrt{95}-6\sqrt{2}+\sqrt{2}\)
=\(\sqrt{95}-\left(6+1\right)\sqrt{2}\)
=\(\sqrt{95}-7\sqrt{2}\)
c\(\sqrt{99}-\sqrt{11}+2\sqrt{44}\)
=\(3\sqrt{11}-\sqrt{11}+4\sqrt{11}\)
=\(\left(3-1+4\right)\sqrt{11}\)
=\(6\sqrt{11}\)