VT = \(2\sqrt{2}\left(2-3\sqrt{3}\right)+\left(1-2\sqrt{2}\right)^2+6\sqrt{6}\)
\(=4\sqrt{2}-6\sqrt{6}+1-4\sqrt{2}+8+6\sqrt{6}=9\)=VP (đpcm)
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Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
Chứng minh
\(\left(\sqrt{4}-\sqrt{3}\right)^2=\sqrt{49}-\sqrt{48}\)
\(2\sqrt{2}\left(2-3\sqrt{3}\right)+\left(1-2\sqrt{2}\right)^2+6\sqrt{6}=9\)
\(\sqrt{8-2\sqrt{15}-\sqrt{8+2\sqrt{15}}}=-2\sqrt{3}\)
rg: \(\sqrt{\left(\sqrt{7}-4\right)}^2\) = 3
chứng minh:
\(\left(\sqrt{8}-5\sqrt{2}+\sqrt{20}\right)\sqrt{5}-\left(3\sqrt{\dfrac{1}{10}}+10\right)=3.3\sqrt{10}\)
\(\left(\sqrt{12}-6\sqrt{3}+\sqrt{24}\right)\sqrt{6}\left(5\sqrt{\dfrac{1}{2}}+12\right)=-14.5\sqrt{2}\)
1. Tính giá trị biểu thức: Asqrt{a^2+4ab^2+4b}-sqrt{4a^2-12ab^2+9b^4} với asqrt{2} ; b1
2. Đặt Msqrt{57+40sqrt{2}} ; Nsqrt{57-40sqrt{2}}. Tính giá trị của các biểu thức sau:
a) M-N
b) M^3-N^3
3. Chứng minh: left(frac{xsqrt{x}+3sqrt{3}}{x-sqrt{3x}+3}-2sqrt{x}right)left(frac{sqrt{x}+sqrt{3}}{3-x}right)1 (với xge0 và xne3)
4. Chứng minh: frac{left(sqrt{a}-sqrt{b}right)^2+4sqrt{ab}}{sqrt{a}+sqrt{b}}.frac{asqrt{b}-bsqrt{a}}{sqrt{ab}}a-b (a 0 ; b 0)
5. Chứng minh: sqrt{9+4sqrt{2}}2sqrt{2}+1 ;...
Đọc tiếp
1. Tính giá trị biểu thức: \(A=\sqrt{a^2+4ab^2+4b}-\sqrt{4a^2-12ab^2+9b^4}\) với \(a=\sqrt{2}\) ; \(b=1\)
2. Đặt \(M=\sqrt{57+40\sqrt{2}}\) ; \(N=\sqrt{57-40\sqrt{2}}\). Tính giá trị của các biểu thức sau:
a) M-N
b) \(M^3-N^3\)
3. Chứng minh: \(\left(\frac{x\sqrt{x}+3\sqrt{3}}{x-\sqrt{3x}+3}-2\sqrt{x}\right)\left(\frac{\sqrt{x}+\sqrt{3}}{3-x}\right)=1\) (với \(x\ge0\) và \(x\ne3\))
4. Chứng minh: \(\frac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}.\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}=a-b\) (a > 0 ; b > 0)
5. Chứng minh: \(\sqrt{9+4\sqrt{2}}=2\sqrt{2}+1\) ; \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=5+3\sqrt{2}\) ; \(3-2\sqrt{2}=\left(1-\sqrt{2}\right)^2\)
6. Chứng minh: \(\left(\frac{1}{2\sqrt{2}-\sqrt{7}}-\left(3\sqrt{2}+\sqrt{17}\right)\right)^2=\left(\frac{1}{2\sqrt{2}-\sqrt{17}}-\left(2\sqrt{2}-\sqrt{17}\right)\right)^2\)
7. Chứng minh đẳng thức: \(\left(\frac{3\sqrt{2}-\sqrt{6}}{\sqrt{27}-3}-\frac{\sqrt{150}}{3}\right).\frac{1}{\sqrt{6}}=-\frac{4}{3}\)
8.Chứng minh: \(\frac{2002}{\sqrt{2003}}+\frac{2003}{\sqrt{2002}}>\sqrt{2002}+\sqrt{2003}\)
9. Chứng minh rằng: \(\sqrt{2000}-2\sqrt{2001}+\sqrt{2002}< 0\)
10. \(\frac{1}{2}+\frac{1}{3\sqrt{2}}+...+\frac{1}{\left(n+1\right)\sqrt{n}}< 2\) ; \(\frac{7}{5}< \frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}< \frac{29}{30}\)
Tính:A2sqrt{left(-3right)^6}+2sqrt{left(-2right)^4}-4sqrt{left(-2right)^6}Bsqrt{left(sqrt{2}-2right)^2}+sqrt{left(sqrt{2}-3right)^2}Csqrt{left(3-sqrt{3}right)^2}-sqrt{left(1+sqrt{3}right)^2}Dsqrt{left(5+sqrt{6}right)^2}-sqrt{left(sqrt{6}-5right)^2}Esqrt{17^2-8^2}-sqrt{3^2+4^2}
Đọc tiếp
Tính:
\(A=2\sqrt{\left(-3\right)^6}+2\sqrt{\left(-2\right)^4}-4\sqrt{\left(-2\right)^6}\)
\(B=\sqrt{\left(\sqrt{2}-2\right)^2}+\sqrt{\left(\sqrt{2}-3\right)^2}\)
\(C=\sqrt{\left(3-\sqrt{3}\right)^2}-\sqrt{\left(1+\sqrt{3}\right)^2}\)
\(D=\sqrt{\left(5+\sqrt{6}\right)^2}-\sqrt{\left(\sqrt{6}-5\right)^2}\)
\(E=\sqrt{17^2-8^2}-\sqrt{3^2+4^2}\)
frac{3+2sqrt{3}}{sqrt{3}}+frac{2+sqrt{2}}{sqrt{2}+1}-left(sqrt{2}+3right)
0.1cdotsqrt{left(-3right)^2}cdotleft[6sqrt{left(frac{1}{3}right)^2}-sqrt{left(sqrt{3}-2right)^2}right]^2
left(frac{3sqrt{2}+sqrt{6}}{sqrt{12}+2}-frac{sqrt{54}}{3}right)cdotfrac{2}{sqrt{6}}
left(frac{3+2sqrt{3}}{sqrt{3}+2}+frac{2+sqrt{2}}{sqrt{2}+1}right)divleft(1divfrac{1}{sqrt{2}+sqrt{3}}right)
sqrt{frac{5+2sqrt{6}}{5-2sqrt{6}}}+sqrt{frac{5-2sqrt{6}}{5+2sqrt{6}}}
Đọc tiếp
\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(\sqrt{2}+3\right)\)
\(0.1\cdot\sqrt{\left(-3\right)^2}\cdot\left[6\sqrt{\left(\frac{1}{3}\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\right]^2\)
\(\left(\frac{3\sqrt{2}+\sqrt{6}}{\sqrt{12}+2}-\frac{\sqrt{54}}{3}\right)\cdot\frac{2}{\sqrt{6}}\)
\(\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right)\div\left(1\div\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
7 tháng 7 2021 lúc 15:57
Bài 1: Rút gọn3sqrt{9a^6}-6a^3 (với mọi a)sqrt{left(x-1right)^2}+sqrt{left(1-3xright)^2} (Với dfrac{1}{3} x ≤ 1 )sqrt{2-sqrt{3}}.left(sqrt{6}+sqrt{2}right)left(sqrt{10}+sqrt{2}right)left(6-2sqrt{5}right)sqrt{3+sqrt{5}}sqrt{23-8sqrt{7}}+sqrt{8-2sqrt{7}}sqrt{x+2sqrt{x-1}}+sqrt{x-2sqrt{x-1}} (với 1x2)sqrt{x+4sqrt{x-4}}+sqrt{x-4sqrt{x-4}} (với x ≥4)
Đọc tiếp
Bài 1: Rút gọn
\(3\sqrt{9a^6}-6a^3\) (với mọi a)
\(\sqrt{\left(x-1\right)^2}+\sqrt{\left(1-3x\right)^2}\) (Với \(\dfrac{1}{3}\) < x ≤ 1 )
\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
\(\left(\sqrt{10}+\sqrt{2}\right)\left(6-2\sqrt{5}\right)\sqrt{3+\sqrt{5}}\)
\(\sqrt{23-8\sqrt{7}}+\sqrt{8-2\sqrt{7}}\)
\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\) (với 1<x<2)
\(\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}\) (với x ≥4)
Tính:Asqrt{27}-2sqrt{48}+3sqrt{75}Bsqrt{left(sqrt{5}-2right)^2}-sqrt{left(sqrt{5}-3right)^2}Csqrt{left(2sqrt{3}+1right)^2}+sqrt{left(2sqrt{3}-5right)^2}Dsqrt{9-4sqrt{5}}-sqrt{14+6sqrt{5}}Edfrac{4}{sqrt{5}-2}-dfrac{32}{sqrt{5}+1}Mdfrac{10}{3sqrt{2}-4}+dfrac{28}{3sqrt{2}+2} please help ;-;
Đọc tiếp
Tính:
\(A=\sqrt{27}-2\sqrt{48}+3\sqrt{75}\)
\(B=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{\left(\sqrt{5}-3\right)^2}\)
\(C=\sqrt{\left(2\sqrt{3}+1\right)^2}+\sqrt{\left(2\sqrt{3}-5\right)^2}\)
\(D=\sqrt{9-4\sqrt{5}}-\sqrt{14+6\sqrt{5}}\)
\(E=\dfrac{4}{\sqrt{5}-2}-\dfrac{32}{\sqrt{5}+1}\)
\(M=\dfrac{10}{3\sqrt{2}-4}+\dfrac{28}{3\sqrt{2}+2}\)
please help ;-;
a) sqrt{3^2}-sqrt{left(7right)^2}+sqrt{left(-1right)^2}
b)-2sqrt{left(-2right)^2}+sqrt{left(-5right)^2}+sqrt{3^2}
c)sqrt{left(2-sqrt{2}right)^2}+sqrt{left(2+sqrt{2}right)^2}
d)sqrt{left(3sqrt{2}right)^2}-sqrt{left(1-sqrt{2}right)^2}
e)sqrt{3-2sqrt{2}}+sqrt{3+2sqrt{2}}
f)sqrt{9-4sqrt{5}}+sqrt{9+4sqrt{5}}
g)sqrt{9-4sqrt{2}}+sqrt{11-6sqrt{2}}
h)sqrt{12+8sqrt{2}}+sqrt{6-4sqrt{2}}
k)left(2-sqrt{3}right)sqrt{7+4sqrt{3}}
Đọc tiếp
a) \(\sqrt{3^2}-\sqrt{\left(7\right)^2}+\sqrt{\left(-1\right)^2}\)
b)\(-2\sqrt{\left(-2\right)^2}+\sqrt{\left(-5\right)^2}+\sqrt{3^2}\)
c)\(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(2+\sqrt{2}\right)^2}\)
d)\(\sqrt{\left(3\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
e)\(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\)
f)\(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
g)\(\sqrt{9-4\sqrt{2}}+\sqrt{11-6\sqrt{2}}\)
h)\(\sqrt{12+8\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
k)\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\)
Rút gọn các biểu thức sau:
\(D=\left(\dfrac{5\sqrt{x}-6}{x-9}-\dfrac{2}{\sqrt{x}+3}\right):\left(1+\dfrac{6}{x-9}\right)\)
\(F=\left(\dfrac{3}{\sqrt{1}+x}+\sqrt{1-x}\right):\left(\dfrac{3}{\sqrt{1-x^2}}+1\right)\)