Chương I - Căn bậc hai. Căn bậc ba
Các câu hỏi tương tự
tính:giải chi tiết nha
\(\sqrt{29-4\sqrt{7}}\)
\(\sqrt{19+6\sqrt{2}}\)
\(\sqrt{28-6\sqrt{3}}\)
\(\sqrt{46-6\sqrt{5}}\)
\(\sqrt{49+8\sqrt{3}}\)
\(\sqrt{32-8\sqrt{7}}\)
1,Chứng minh
a,11+\(6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
b,\(8-2\sqrt{7}=\left(\sqrt{7}-1\right)^2\)
c,\(\left(5-\sqrt{3}\right)^2=28-10\sqrt{3}\)
d,\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}=2\)
1) \(\sqrt{7-2\sqrt{10}}\) - \(\sqrt{7+2\sqrt{10}}\)
2) \(\sqrt{4-2\sqrt{3}}\) + \(\sqrt{4+2\sqrt{3}}\)
3) \(\sqrt{6-4\sqrt{2}}\) + \(\sqrt{22-12\sqrt{2}}\)
Rút gọn
1, 3sqrt{3}.left(3+2sqrt{6}-sqrt{33}right)
2, sqrt{2}.left(sqrt{8}-sqrt{32}+3sqrt{18}right)
3, left(2sqrt{28}-3sqrt{7}+5sqrt{63}right).sqrt{112}
4, left(5sqrt{6}-4sqrt{10}+7sqrt{30}right):sqrt{2}
5, left(5sqrt{3}+3sqrt{5}right):sqrt{15}
6, left(1+sqrt{3}-sqrt{2}right).left(1+sqrt{3}+sqrt{2}right)
7, left(4sqrt{27}-2sqrt{48}-5sqrt{75}right):2sqrt{3}
Các bạn ơi ! giúp mik với đi !!!
Đọc tiếp
Rút gọn
1, \(3\sqrt{3}.\left(3+2\sqrt{6}-\sqrt{33}\right)\)
2, \(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
3, \(\left(2\sqrt{28}-3\sqrt{7}+5\sqrt{63}\right).\sqrt{112}\)
4, \(\left(5\sqrt{6}-4\sqrt{10}+7\sqrt{30}\right):\sqrt{2}\)
5, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
6, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)
7, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)
Các bạn ơi ! giúp mik với đi !!!
rút gọn biểu thức
a) frac{3}{2+sqrt{3}}+frac{13}{4-sqrt{3}}+frac{6}{sqrt{3}}
b) left(frac{sqrt{14}-sqrt{7}}{sqrt{2}-1}+frac{sqrt{15}-sqrt{5}}{sqrt{3}-1}right):frac{1}{sqrt{7}-sqrt{5}}
c) sqrt{left(2+sqrt{3}right)^2}-sqrt{28-10sqrt{3}}
d) frac{3}{3+2sqrt{3}}+frac{3}{3-2sqrt{3}}
e) sqrt{20}-15sqrt{frac{1}{5}}+sqrt{left(1-sqrt{5}right)^2}
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rút gọn biểu thức
a) \(\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)
b) \(\left(\frac{\sqrt{14}-\sqrt{7}}{\sqrt{2}-1}+\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
c) \(\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{28-10\sqrt{3}}\)
d) \(\frac{3}{3+2\sqrt{3}}+\frac{3}{3-2\sqrt{3}}\)
e) \(\sqrt{20}-15\sqrt{\frac{1}{5}}+\sqrt{\left(1-\sqrt{5}\right)^2}\)
a) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\sqrt{7}+7\sqrt{8}\)
b) \(\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):10\)
c) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\left(\sqrt{2}-3\sqrt{0,4}\right)\)
thực hiện các phép tính trên
Đưa thừa số ra ngoài dấu căn
a.
\(\left(\sqrt{28}-5\sqrt{35}+7\sqrt{112}\right)2\sqrt{7}\)
b. \(\left(\sqrt{72}-3\sqrt{24}+5\sqrt{8}\right)\sqrt{2}+4\sqrt{27}\)
Bài 5: Rút gọn căn cho một số bằng phép khai phương
9 sqrt{12} + sqrt{75} - sqrt{27}
10 sqrt{27} - sqrt{12} + sqrt{75} + sqrt{147}
11 2sqrt{3} + sqrt{48} - sqrt{75} - sqrt{243}
12 sqrt{5+2sqrt{6}} - sqrt{5-2sqrt{6}}
13 sqrt{9-4sqrt{5}} - sqrt{9+sqrt{80}}
14 sqrt{3+2sqrt{2}} _ sqrt{6-4sqrt{2}}
15 sqrt{17-4sqrt{9+4sqrt{5}}}
16 sqrt{4+sqrt{5}sqrt{3}+5sqrt{48-10sqrt{7+4sqrt{3}}}}
17 (sqrt{28} - 2sqrt{14} + sqrt{7})sqrt{7} + 7sqrt{8}
18 sqrt{left(sqrt{14}-3sqrt{2}right)^2}+6sqrt{28}
19 df...
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Bài 5: Rút gọn căn cho một số bằng phép khai phương
9> \(\sqrt{12}\) + \(\sqrt{75}\) - \(\sqrt{27}\)
10> \(\sqrt{27}\) - \(\sqrt{12}\) + \(\sqrt{75}\) + \(\sqrt{147}\)
11> \(2\sqrt{3}\) + \(\sqrt{48}\) - \(\sqrt{75}\) - \(\sqrt{243}\)
12> \(\sqrt{5+2\sqrt{6}}\) - \(\sqrt{5-2\sqrt{6}}\)
13> \(\sqrt{9-4\sqrt{5}}\) - \(\sqrt{9+\sqrt{80}}\)
14> \(\sqrt{3+2\sqrt{2}}\) _ \(\sqrt{6-4\sqrt{2}}\)
15> \(\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
16> \(\sqrt{4+\sqrt{5}\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
17> (\(\sqrt{28}\) - \(2\sqrt{14}\) + \(\sqrt{7}\))\(\sqrt{7}\) + 7\(\sqrt{8}\)
18> \(\sqrt{\left(\sqrt{14}-3\sqrt{2}\right)^2}+6\sqrt{28}\)
19> \(\dfrac{1}{\sqrt{5}-2}\) + \(\dfrac{1}{\sqrt{5}+2}\)
20> \(\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5-\sqrt{3}}}\) + \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)
21> \(\dfrac{1}{4-3\sqrt{2}}\) _ \(\dfrac{1}{4+3\sqrt{2}}\)
22> \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
\(A=\sqrt{28}-\sqrt{63}+\dfrac{7+\sqrt{7}}{\sqrt{7}}-\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(B=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{1}{\sqrt{x}-3}\right)\dfrac{4\sqrt{x}+12}{\sqrt{x}}\) (ĐK x>0; x\(\ne9\))
a)Rút gọn A và B
b) Tìm các giá trị của x để giá trị biểu thức A lớn hơn giá trị biểu thức B