\(=1+\sqrt{3}+\sqrt{3-2\sqrt{3}.1+1}=1+\sqrt{3}+\sqrt{\left(\sqrt{3}-1\right)^2}=1+\sqrt{3}+\sqrt{3}-1=2\sqrt{3}\)
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Thực hiện phép tínha)sqrt{left(sqrt{2}-1right)^2}+sqrt{left(3sqrt{2}-2right)^2}b)2.sqrt{left(sqrt{3}-1right)^2}-sqrt{left(2sqrt{3}+1right)^2}c)4.sqrt{left(2-dfrac{sqrt{3}}{2}right)^2}-3.sqrt{left(sqrt{3}-1right)^2}d)sqrt{3+2sqrt{2}}+sqrt{3-2sqrt{2}}e)left(sqrt{3}-1right)^2+left(2sqrt{3}+1right)^2g)left(1-2sqrt{2}right)^2-left(sqrt{2}+1right)^2
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Thực hiện phép tính
a)\(\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}\)
b)\(2.\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{\left(2\sqrt{3}+1\right)^2}\)
c)\(4.\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3.\sqrt{\left(\sqrt{3}-1\right)^2}\)
d)\(\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}\)
e)\(\left(\sqrt{3}-1\right)^2+\left(2\sqrt{3}+1\right)^2\)
g)\(\left(1-2\sqrt{2}\right)^2-\left(\sqrt{2}+1\right)^2\)
30 tháng 9 2021 lúc 22:00
1. Tính
a. \(\left(3\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-3\sqrt{2}\right)\)
b. \(\dfrac{1}{\sqrt{2013}-\sqrt{2014}}-\dfrac{1}{\sqrt{2014}-\sqrt{2015}}\)
c. \(\sqrt{\left(4+\sqrt{10}\right)^2}-\sqrt{\left(4-\sqrt{10}\right)^2}\)
d. \(\sqrt{3-2\sqrt{2}}+\sqrt{6-4\sqrt{2}}+\sqrt{9-4\sqrt{2}}\)
1> Rut gon
a)\(\sqrt{6-2\sqrt{2}+2\sqrt{3}-2\sqrt{6}}\)
b) \(\left(\sqrt{2}+1\right)\left(\left(\sqrt{2}\right)^2+1\right)\left(\left(\sqrt{2}\right)^4+1\right)\left(\left(\sqrt{2}\right)^8+1\right)\left(\left(\sqrt{2}\right)^{16}+1\right)\)
c)\(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
d) \(\sqrt{3-\frac{4\sqrt{5}}{3}}+\sqrt{3+\frac{4\sqrt{5}}{3}}\)
Rút gọn biểu thức 1) frac{sqrt{5+2sqrt{6}}+sqrt{8+2sqrt{15}}}{sqrt{7+2sqrt{10}}}2) left(2+frac{3+sqrt{3}}{sqrt{3}+1}right)left(2+frac{3-sqrt{3}}{sqrt{3}-1}right):left(sqrt{5}-2right)3) left(frac{15}{sqrt{6}+1}+frac{4}{sqrt{6}-2}-frac{12}{3-sqrt{6}}right).left(sqrt{6}+11right)4) frac{1}{1+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+...+frac{1}{sqrt{99}+sqrt{100}}5) frac{1}{1-sqrt{2}}-frac{1}{sqrt{2}-sqrt{3}}+frac{1}{sqrt{3}-sqrt{4}}-...-frac{1}{sqrt{98}-sqrt{99}}+frac{1}{sqrt{99}-s...
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Rút gọn biểu thức
1) \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8+2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
2) \(\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right):\left(\sqrt{5}-2\right)\)
3) \(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
4) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
5) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...-\frac{1}{\sqrt{98}-\sqrt{99}}+\frac{1}{\sqrt{99}-\sqrt{100}}\)
6) \(\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
7)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)
Thực hiện phép tính.1) sqrt[3]{sqrt{2}+1}.sqrt[3]{3+2sqrt{2}}:sqrt[3]{left(4-2sqrt{3}right)left(sqrt{3}-1right)}2) left(frac{1}{2}.sqrt[3]{9}-2.sqrt[3]{3}+3.sqrt[3]{frac{1}{3}}right):2.sqrt[3]{frac{1}{3}}3) left(sqrt[3]{4}+1right)^3-left(sqrt[3]{4}-1right)^34) left(2sqrt{6}-4sqrt{3}+5sqrt{2}-frac{1}{4}sqrt{8}right).3sqrt{6}
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Thực hiện phép tính.
1) \(\sqrt[3]{\sqrt{2}+1}.\sqrt[3]{3+2\sqrt{2}}:\sqrt[3]{\left(4-2\sqrt{3}\right)\left(\sqrt{3}-1\right)}\)
2) \(\left(\frac{1}{2}.\sqrt[3]{9}-2.\sqrt[3]{3}+3.\sqrt[3]{\frac{1}{3}}\right):2.\sqrt[3]{\frac{1}{3}}\)
3) \(\left(\sqrt[3]{4}+1\right)^3-\left(\sqrt[3]{4}-1\right)^3\)
4) \(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\frac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
Thực hiện pháp tính
\(\sqrt[3]{\left(\sqrt{2}+1\right)\left(3+2\sqrt{2}\right)}\)
\(\sqrt[3]{(4-2\sqrt{3})\left(\sqrt{3}-1\right)}\)
\(\left(\sqrt[3]{4}+1\right)^3-\left(\sqrt[3]{4}-1\right)^3\)
\(\left(\sqrt[3]{9}-\sqrt[3]{6}+\sqrt[3]{4}\right)\left(\sqrt[3]{3}+\sqrt[3]{2}\right)\)
giải pt
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)}\)=3x-1
Gấp lắm . Giúp mình cảm ơn ạBài 1 2sqrt{left(1+sqrt{3}right)^{ }3}-sqrt{left(2sqrt{3}-3right)^2}left(1+sqrt{3}-sqrt{5}right).left(1+sqrt{3}+sqrt{5}right)left(sqrt[]{dfrac{8}{3}}-sqrt{5}right)xsqrt{6}left(5+4sqrt{2}right).left(3+2sqrt{1}+sqrt{2}right).left(3-2sqrt{1}+2right)sqrt{3+2sqrt{2}}-sqrt{3-2sqrt{2}}
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Gấp lắm . Giúp mình cảm ơn ạ
Bài 1
\(2\sqrt{\left(1+\sqrt{3}\right)^{ }3}-\sqrt{\left(2\sqrt{3}-3\right)^2}\)
\(\left(1+\sqrt{3}-\sqrt{5}\right).\left(1+\sqrt{3}+\sqrt{5}\right)\)
\(\left(\sqrt[]{\dfrac{8}{3}}-\sqrt{5}\right)x\sqrt{6}\)
\(\left(5+4\sqrt{2}\right).\left(3+2\sqrt{1}+\sqrt{2}\right).\left(3-2\sqrt{1}+2\right)\)
\(\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}\)
Giải phương trình:
\(\frac{2\left(x-\sqrt{3}\right)\left(x-\sqrt{2}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\)
Giải phương trình :
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\) .