Tính:
\(\left(\sqrt{14}-\sqrt{2}\right)\sqrt{4+\sqrt{7}}\)
ND
Những câu hỏi liên quan
Tính :
1)\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
2)\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
3)\(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right).\sqrt{\sqrt{3}+2}\)
4)\(\left(5+\sqrt{21}\right).\left(\sqrt{14}-\sqrt{6}\right).\sqrt{5-\sqrt{21}}\)
a)\(\left(\sqrt{21}+7\right)\cdot\sqrt{10-2\sqrt{21}}\)
\(=\left(\sqrt{21}+7\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
\(=\sqrt{7}\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{7}\left(7-3\right)=4\sqrt{7}\)
b)\(\left(7+\sqrt{14}\right)\sqrt{9-2\sqrt{14}}\)
\(=\left(7+\sqrt{14}\right)\sqrt{\left(\sqrt{7}-\sqrt{2}\right)^2}\)
\(=\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right)\left(\sqrt{7}-\sqrt{2}\right)\)
\(=\sqrt{7}\left(7-2\right)=5\sqrt{7}\)
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\(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\sqrt{4+\sqrt{7}}\)
\(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)
\(=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{8+2\sqrt{7}}\right)\)
\(=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{\left(\sqrt{7}+1\right)^2}\right)\)
\(=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)^2\)
\(=\left(4-\sqrt{7}\right)\left(8+2\sqrt{7}\right)\)
\(=2\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)\)
\(=2\left(16-7\right)=2.9=18\)
Vậy : \(\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)=18\)
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Rút gọn các biểu thức sau:a) left(sqrt{8}-3sqrt{2}+sqrt{10}right)left(sqrt{2}-3sqrt{0,4}right) b) left(sqrt{28}-2sqrt{14}+sqrt{7}right).sqrt{7}+7sqrt{8}c) 2sqrt{left(sqrt{2}-3right)^2}+sqrt{2left(-3right)^2}-5sqrt{left(-1right)^4} d) left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}
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Rút gọn các biểu thức sau:
a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\left(\sqrt{2}-3\sqrt{0,4}\right)\) b) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
c) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}\) d) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
1.sqrt{frac{129}{16}+sqrt{2}}
2.sqrt{frac{289+4sqrt{72}}{16}}
3. sqrt{2-sqrt{3}}.left(sqrt{6}+sqrt{2}right)
4.left(sqrt{21}+7right).sqrt{10-2sqrt{21}}
5.2.left(sqrt{10}-sqrt{2}right).sqrt{4+sqrt{6-2sqrt{5}}}
6.left(4sqrt{2}+sqrt{30}right).left(sqrt{5}-sqrt{3}right).sqrt{4-sqrt{15}}
7.left(7+sqrt{14}right).sqrt{9-2sqrt{14}}
Đọc tiếp
1.\(\sqrt{\frac{129}{16}+\sqrt{2}}\)
2.\(\sqrt{\frac{289+4\sqrt{72}}{16}}\)
3. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
4.\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
5.\(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
6.\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)
7.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
1. Đặt A =\(\sqrt{\frac{129}{16}+\sqrt{2}}\)
\(\sqrt{16}\)A = \(\sqrt{129+16\sqrt{2}}\)
4A = \(\sqrt{\left(8\sqrt{2}+1\right)^2}\)
4A = \(8\sqrt{2}+1\)
⇒ A = \(\frac{\text{}8\sqrt{2}+1}{4}\)= \(2\sqrt{2}\) + \(\frac{1}{4}\)
2. Đặt B = \(\sqrt{\frac{289+4\sqrt{72}}{16}}\)
\(\sqrt{16}\)B = \(\sqrt{289+24\sqrt{2}}\)
4B = \(\sqrt{\left(12\sqrt{2}+1\right)^2}\)
4B = \(12\sqrt{2}+1\)
⇒ B = \(\frac{12\sqrt{2}+1}{4}\)= \(3\sqrt{2}+\frac{1}{4}\)
3. \(\sqrt{2-\sqrt{3}}\). \(\left(\sqrt{6}+\sqrt{2}\right)\)
= \(\sqrt{2-\sqrt{3}}\). \(\sqrt{2}.\left(\sqrt{3}+1\right)\)
= \(\sqrt{4-2\sqrt{3}}\) . \(\left(\sqrt{3}+1\right)\)
= \(\sqrt{\left(\sqrt{3}-1\right)^2}\) . \(\left(\sqrt{3}+1\right)\)
= \(\left(\sqrt{3}-1\right)\). \(\left(\sqrt{3}+1\right)\)
= \(\left(\sqrt{3}\right)^2\) - 12
= 3 - 1
= 2
4. \(\left(\sqrt{21}+7\right)\). \(\sqrt{10-2\sqrt{21}}\)
= \(\left(\sqrt{21}+7\right)\) . \(\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)
= \(\sqrt{7}\left(\sqrt{3}+\sqrt{7}\right)\) . \(\left(\sqrt{7}-\sqrt{3}\right)\)
= \(\sqrt{7}\) \(\left[\left(\sqrt{7}\right)^2-\left(\sqrt{3}\right)^2\right]\)
= \(\sqrt{7}\) . (7 - 3)
= 4\(\sqrt{7}\)
5. \(2.\left(\sqrt{10}-\sqrt{2}\right)\). \(\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
= \(2.\left(\sqrt{10}-\sqrt{2}\right)\) . \(\sqrt{4+\sqrt{5}-1}\)
= \(2.\left(\sqrt{10}-\sqrt{2}\right)\) . \(\sqrt{3+\sqrt{5}}\)
= \(\left(\sqrt{10}-\sqrt{2}\right)\) . \(\sqrt{12+4\sqrt{5}}\)
= \(\left(\sqrt{10}-\sqrt{2}\right)\) . \(\left(\sqrt{10}+\sqrt{2}\right)\)
= \(\left(\sqrt{10}\right)^2-\left(\sqrt{2}\right)^2\)
= 10 - 2
= 8
6. \(\left(4\sqrt{2}+\sqrt{30}\right)\). \(\left(\sqrt{5}-\sqrt{3}\right)\). \(\sqrt{4-\sqrt{15}}\)
= \(\sqrt{2}\)\(\left(4+\sqrt{15}\right)\) . \(\left(\sqrt{5}-\sqrt{3}\right)\) . \(\sqrt{4-\sqrt{15}}\)
= \(\left(4+\sqrt{15}\right)\) . \(\left(\sqrt{5}-\sqrt{3}\right)\) . \(\sqrt{8-2\sqrt{15}}\)
= \(\left(4+\sqrt{15}\right)\) . \(\left(\sqrt{5}-\sqrt{3}\right)\) . \(\left(\sqrt{5}-\sqrt{3}\right)\)
= \(\left(4+\sqrt{15}\right)\) . \(\left(\sqrt{5}-\sqrt{3}\right)^2\)
= \(\left(4+\sqrt{15}\right)\). \(\left(8-2\sqrt{15}\right)\)
= 32 - \(8\sqrt{15}\) + \(8\sqrt{15}\) - 30
= 2
7. \(\left(7-\sqrt{14}\right)\) . \(\sqrt{9-2\sqrt{14}}\)
= \(\sqrt{7}\) \(\left(\sqrt{7}-\sqrt{2}\right)\). \(\left(\sqrt{7}-\sqrt{2}\right)\)
= \(\sqrt{7}\). \(\left(\sqrt{7}-\sqrt{2}\right)^2\)
= \(\sqrt{7}\) . \(\left(9-2\sqrt{14}\right)\)
= 9\(\sqrt{7}\) - 14\(\sqrt{2}\)
TICK MÌNH NHA!
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Tính
1.\(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
2. \(\left(\sqrt{8}-\sqrt{2}-\sqrt{5}\right)\left(\sqrt{18}-\sqrt{8}+\sqrt{5}\right)\)
1) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
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Xin lỗi xin lỗi :v
1)\(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
= \(\sqrt{7}.\left(3\sqrt{7}-2\sqrt{14}\right)+14\sqrt{2}\)
= 21 - \(14\sqrt{2}+14\sqrt{2}\)
= 21
2) \(\left(\sqrt{8}-\sqrt{2}-\sqrt{5}\right)\left(\sqrt{18}-\sqrt{8}+\sqrt{5}\right)\)
= \(\left(2\sqrt{2}-\sqrt{2}-\sqrt{5}\right)\left(3\sqrt{2}+\sqrt{5}-2\sqrt{2}\right)\)
= \(\left(\sqrt{2}-\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)\)
=\(\left(\sqrt{2}\right)^2-\left(\sqrt{5}\right)^2\)
= -3
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rút gọn:
\(A=\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)
ta có : \(A=\left(4-\sqrt{7}\right)\left(\sqrt{14}+\sqrt{2}\right)\left(\sqrt{4+\sqrt{7}}\right)\)
\(\Leftrightarrow A=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{8+2\sqrt{7}}\right)\)
\(\Leftrightarrow A=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)\left(\sqrt{\left(\sqrt{7}+1\right)^2}\right)\) \(\Leftrightarrow A=\left(4-\sqrt{7}\right)\left(\sqrt{7}+1\right)^2=\left(4-\sqrt{7}\right)\left(8+2\sqrt{7}\right)\)\(\Leftrightarrow A=2\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)=2\left(16-7\right)=2.9=18\)
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Rút gọn :
dfrac{sqrt{x+sqrt{4left(x-1right)}}-sqrt{x-sqrt{4left(x-1right)}}}{sqrt{x^2-4left(x-1right)}}.left(sqrt{x-1}-dfrac{1}{sqrt{x-1}}right)
b)left(sqrt{2}+1right)left(sqrt{3}+1right)left(sqrt{6}+1right)left(5-2sqrt{2}-sqrt{3}right)
c)left(sqrt{5}+1right)left(sqrt{7}+1right)left(sqrt{35}+1right)left(34-4sqrt{7}-6sqrt{5}right)
d) left(sqrt{7}+1right)left(2sqrt{2}-1right)left(2sqrt{14}-1right)left(55+12sqrt{2}-7sqrt{7}right)
e)left(3sqrt{2}+1right)left(2sqrt{3}+1right)left(6sqrt{6}+1...
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Rút gọn :
\(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
b)\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)
c)\(\left(\sqrt{5}+1\right)\left(\sqrt{7}+1\right)\left(\sqrt{35}+1\right)\left(34-4\sqrt{7}-6\sqrt{5}\right)\)
d) \(\left(\sqrt{7}+1\right)\left(2\sqrt{2}-1\right)\left(2\sqrt{14}-1\right)\left(55+12\sqrt{2}-7\sqrt{7}\right)\)
e)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)
TA
5 tháng 11 2023 lúc 17:00
Tính:( Các bạn bấm máy tính nhé)
1.\(\left(\sqrt{10}-\sqrt{14}\right).\left(\sqrt{6+\sqrt{35}}\right)\)
2. \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2}+\sqrt{2}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
1: \(\left(\sqrt{10}-\sqrt{14}\right)\cdot\sqrt{6+\sqrt{35}}\)
\(=\left(\sqrt{5}-\sqrt{7}\right)\cdot\sqrt{12+2\sqrt{35}}\)
\(=\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}+\sqrt{7}\right)\)
=5-7=-2
2: Sửa đề: \(\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{2^2-\left(2+\sqrt{2}\right)}\)
\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-2-\sqrt{2}}\)
\(=\sqrt{2\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}=\sqrt{2}\)
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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 ;-;
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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 ;-;