Mấy cái bài này là cơ hội để máy tính trổ tài đấy! Cứ nhấn là nó ra, cần gì phải đăng lên đây z?!
D=\(\sqrt{147}\)+\(\sqrt{54}-4\sqrt{27}\)
=\(\sqrt{49.3}+\sqrt{9.6}-4\sqrt{3.9}\)
=\(7\sqrt{3}+3\sqrt{6}-12\sqrt{3}\)
=\(-5\sqrt{3}+3\sqrt{6}\)
Mấy cái bài này là cơ hội để máy tính trổ tài đấy! Cứ nhấn là nó ra, cần gì phải đăng lên đây z?!
D=\(\sqrt{147}\)+\(\sqrt{54}-4\sqrt{27}\)
=\(\sqrt{49.3}+\sqrt{9.6}-4\sqrt{3.9}\)
=\(7\sqrt{3}+3\sqrt{6}-12\sqrt{3}\)
=\(-5\sqrt{3}+3\sqrt{6}\)
thực hiện các phép tính
\(a.\left(\sqrt{12}-\sqrt{48}-\sqrt{108}-\sqrt{192}\right):2\sqrt{3}\)
b.\(\left(2\sqrt{112}-5\sqrt{7}+2\sqrt{63}-2\sqrt{28}\right)\sqrt{7}\)
c.\(\left(2\sqrt{27}-3\sqrt{48}+3\sqrt{75}-\sqrt{192}\right)\left(1-\sqrt{3}\right)\)
d.\(7\sqrt{24}-\sqrt{150}-5\sqrt{54}\)
Tính giá trị các biểu thức:
a.\(\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right)\sqrt{3}\)
b.\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
c.\(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)3\sqrt{6}\)
d.\(3\sqrt{15\sqrt{50}}+5\sqrt{24\sqrt{8}}-4\sqrt{12\sqrt{32}}\)
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:
1) \(\sqrt{12}+5\sqrt{3}-\sqrt{48}\)
2) \(5\sqrt{5}+\sqrt{20}-3\sqrt{45}\)
3) \(2\sqrt{32}+4\sqrt{8}-5\sqrt{18}\)
4) \(3\sqrt{12}-4\sqrt{27}+5\sqrt{48}\)
5) \(\sqrt{12}+\sqrt{75}-\sqrt{27}\)
6) \(2\sqrt{18}-7\sqrt{2}+\sqrt{162}\)
7) \(3\sqrt{20}-2\sqrt{45}+4\sqrt{5}\)
8) \(\left(\sqrt{2}+2\right)\sqrt{2}-2\sqrt{2}\)
9) \(\dfrac{1}{\sqrt{5}-1}-\dfrac{1}{\sqrt{5}+}\)
10) \(\dfrac{1}{\sqrt{5}-2}+\dfrac{1}{\sqrt{5}+2}\)
11) \(\dfrac{2}{4-3\sqrt{2}}-\dfrac{2}{4+3\sqrt{2}}\)
12) \(\dfrac{2+\sqrt{2}}{1+\sqrt{2}}\)
13) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\sqrt{7}+7\sqrt{8}\)
14) \(\left(\sqrt{14}-3\sqrt{2}\right)^2+6\sqrt{28}\)
15) \(\left(\sqrt{6}-\sqrt{5}\right)^2-\sqrt{120}\)
16) \(\left(2\sqrt{3}-3\sqrt{2}\right)^2+2\sqrt{6}+3\sqrt{24}\)
17) \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}+3\right)^2}\)
18) \(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}\)
19) \(\sqrt{\left(\sqrt{5}-3\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
20) \(\left(\sqrt{19}-3\right)\left(\sqrt{19}+3\right)\)
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> \(2\sqrt{3}\) + \(\sqrt{48}\) - \(\sqrt{75}\) - \(\sqrt{243}\)
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> \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{7}\)
Tinh
\(a,\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
\(b,\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
\(c,\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}\)
\(d,\left(\sqrt{6}+2\right)\left(\sqrt{3}-\sqrt{2}\right)\)
\(e,\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
\(f,\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}\)
\(g,\left(\frac{1}{\sqrt{5}-\sqrt{2}}-\frac{1}{\sqrt{5}+\sqrt{2}}+1\right)\frac{1}{\left(\sqrt{2}+1\right)^2}\)
A,√(1\√2-1/2)^2
B,√33-8√7
C,√(0,1-√0,1)^2
D,6√7+16
E,√1/√5-1/2)^2-1/√5
G,√27-8√11
F√7-4√3
Tính:
1)a)\(2\sqrt{40.\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{548}\)
b)\(\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right):\sqrt{15}\)
d)\(\left(12\sqrt{50}-8\sqrt{200}+7\sqrt{450}\right):\sqrt{10}\)
e) (\(\sqrt{\dfrac{1}{7}}-\sqrt[]{\dfrac{16}{7}}+\sqrt[]{\dfrac{9}{7}}\)):\(\sqrt{7}\)
2)
a)A=\(\sqrt{3+\sqrt{5+2\sqrt{3}}}.\sqrt{3-\sqrt[]{5+2\sqrt[]{3}}}\)
b) B=\(\sqrt{4+\sqrt{8}}\) . \(\sqrt{2+\sqrt{2+\sqrt{2}}}\) .\(\sqrt{2-\sqrt{2+\sqrt{2}}}\)