BT1: Tính
a, \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{12}\)
b, \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
BT2: Rút gọn
\(3x-\sqrt{27}+\frac{\sqrt{x^3+3x^2}}{\sqrt{x+3}}\) ( x ≥ 0 )
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Những câu hỏi liên quan
13 tháng 8 2020
Bài 1:
a) Ta có: \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
\(=\frac{\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}-2}{\sqrt{2}}\)
\(=\frac{\sqrt{5+2\cdot\sqrt{5}\cdot1+1}-\sqrt{5-2\cdot\sqrt{5}\cdot1+1}-2}{\sqrt{2}}\)
\(=\frac{\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{\left(\sqrt{5}-1\right)^2}-2}{\sqrt{2}}\)
\(=\frac{\left|\sqrt{5}+1\right|-\left|\sqrt{5}-1\right|-2}{\sqrt{2}}\)
\(=\frac{\sqrt{5}+1-\left(\sqrt{5}-1\right)-2}{\sqrt{2}}\)(Vì \(\sqrt{5}>1>0\))
\(=\frac{\sqrt{5}+1-\sqrt{5}+1-2}{\sqrt{2}}=\frac{2-2}{\sqrt{2}}=\frac{0}{\sqrt{2}}=0\)
b) Ta có: \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
\(=\sqrt{\frac{7}{2}-2\cdot\sqrt{\frac{7}{2}}\cdot\sqrt{\frac{1}{2}}+\frac{1}{2}}-\sqrt{\frac{7}{2}+2\cdot\sqrt{\frac{7}{2}}\cdot\sqrt{\frac{1}{2}}+\frac{1}{2}}+\sqrt{7}\)
\(=\sqrt{\left(\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}\right)^2}-\sqrt{\left(\sqrt{\frac{7}{2}}+\sqrt{\frac{1}{2}}\right)^2}+\sqrt{7}\)
\(=\left|\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}\right|-\left|\sqrt{\frac{7}{2}}+\sqrt{\frac{1}{2}}\right|+\sqrt{7}\)
\(=\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}-\left(\sqrt{\frac{7}{2}}+\sqrt{\frac{1}{2}}\right)+\sqrt{7}\)(Vì \(\sqrt{\frac{7}{2}}>\sqrt{\frac{1}{2}}>0\))
\(=\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}-\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}+\sqrt{7}\)
\(=-2\sqrt{\frac{1}{2}}+\sqrt{7}\)
\(=-\sqrt{2}+\sqrt{7}\)
9 tháng 11 2021
\(a,=27-5\sqrt{3x}\\ b,=3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}+28=14\sqrt{2x}+28\)
H9
HT.Phong (9A5)
CTVHS
24 tháng 7 2023
9) Sửa: \(2\sqrt{8\sqrt{3}}-2\sqrt{5\text{ }\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
\(=2\sqrt{2^2\cdot2\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{2^2\cdot5\sqrt{3}}\)
\(=2\cdot2\sqrt{2\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\cdot2\sqrt{5\sqrt{3}}\)
\(=4\sqrt{2\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}\)
\(=4\sqrt{2\sqrt{3}}-8\sqrt{5\sqrt{3}}\)
10) \(\sqrt{12x}-\sqrt{48x}-3\sqrt{3x}+27\)
\(=\sqrt{2^2\cdot3x}-\sqrt{4^2\cdot3x}-3\sqrt{3x}+27\)
\(=2\sqrt{3x}-4\sqrt{3x}-3\sqrt{3x}+27\)
\(=-5\sqrt{3x}++27\)
11) \(\sqrt{18x}-5\sqrt{8x}+7\sqrt{18x}+28\)
\(=\sqrt{3^2\cdot2x}-5\sqrt{2^2\cdot2x}+7\sqrt{3^2\cdot2x}+28\)
\(=3\sqrt{2x}-5\cdot2\sqrt{2x}+7\cdot3\sqrt{2x}+28\)
\(=3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}+28\)
\(=14\sqrt{2x}+28\)
12) \(\sqrt{45a}-\sqrt{20a}+4\sqrt{45a}+\sqrt{a}\)
\(=\sqrt{3^2\cdot5a}-\sqrt{2^2\cdot5a}+4\sqrt{3^2\cdot5a}+\sqrt{a}\)
\(=3\sqrt{5a}-2\sqrt{5a}+4\cdot3\sqrt{5a}+\sqrt{a}\)
\(=3\sqrt{5a}-2\sqrt{5a}+12\sqrt{5a}+\sqrt{a}\)
\(=13\sqrt{5a}+\sqrt{a}\)
NM
23 tháng 4 2021
Rút gọn các biểu thức sau với x≥0x≥0:
a) 2\(\sqrt{3x}\)-4\(\sqrt{3x}\)+27-3\(\sqrt{3x}\)=27-5\(\sqrt{3x}\)
b)3\(\sqrt{2x}\)-5\(\sqrt{8x}\)+7\(\sqrt{18x}\)+28
=3\(\sqrt{2x}\)-10\(\sqrt{2x}\)+21\(\sqrt{2x}\)+28
=14\(\sqrt{2x}\)+28=14(\(\sqrt{2x}\)+2)
QT
23 tháng 4 2021
a) \(2\sqrt{3x}-4\sqrt{3x}+27-3\sqrt{3x}\)
\(=\left(2\sqrt{3x}-4\sqrt{3x}-3\sqrt{3x}\right)+27\)
\(=-5\sqrt{3x}+27\)
5 tháng 7 2021
a) Ta có: \(A=3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}+30\)
\(=3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}+30\)
\(=14\sqrt{2x}+30\)
b) Ta có: \(B=4\sqrt{\dfrac{25x}{4}}-\dfrac{8}{3}\sqrt{\dfrac{9x}{4}}-\dfrac{4}{3x}\cdot\sqrt{\dfrac{9x^3}{64}}\)
\(=4\cdot\dfrac{5\sqrt{x}}{2}-\dfrac{8}{3}\cdot\dfrac{3\sqrt{x}}{2}-\dfrac{4}{3x}\cdot\dfrac{3x\sqrt{x}}{8}\)
\(=10\sqrt{x}-4\sqrt{x}-\dfrac{1}{2}\sqrt{x}\)
\(=\dfrac{11}{2}\sqrt{x}\)
c) Ta có: \(\dfrac{y}{2}+\dfrac{3}{4}\sqrt{9y^2-6y+1}-\dfrac{3}{2}\)
\(=\dfrac{1}{2}y+\dfrac{3}{4}\left(1-3y\right)-\dfrac{3}{2}\)
\(=\dfrac{1}{2}y+\dfrac{3}{4}-\dfrac{9}{4}y-\dfrac{3}{2}\)
\(=-\dfrac{7}{4}y-\dfrac{3}{4}\)
em cảm mơn nhìu nhìu 
KH
4 tháng 7 2021
\(1.\\ A=\sqrt{\left(2+\sqrt{3}\right)^2}+\sqrt{\left(2-\sqrt{3}\right)^2}\\ =\left|2+\sqrt{3}\right|+\left|2-\sqrt{3}\right|\\ =2+\sqrt{3}+2-\sqrt{3}=4\)
\(2.\\a.\\ P=3x-\sqrt{\left(x-5\right)^2}=3x-\left|x-5\right|\\ b.\\ x=2\Rightarrow P=3\)
\(3.\\ M=\dfrac{\sqrt{\left(x-1\right)^2}}{x-1}=\dfrac{\left|x-1\right|}{x-1}\)
\(\cdot x>1\Rightarrow M=1\\ \cdot x=1\Rightarrow M=0\\\cdot x< 1\Rightarrow M=-1\)
4 tháng 7 2021
B1.
Ta có:A\(=\sqrt{3+4\sqrt{3}+4}+\sqrt{3-4\sqrt{3}+4}\)
\(=\sqrt{\left(\sqrt{3}+2\right)^2}+\sqrt{\left(\sqrt{3}-2\right)^2}\)
\(=\sqrt{3}+2+\sqrt{3}-2=2\sqrt{3}\)