\(\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}\)
\(=\left[\left(\sqrt{15}\right)^2+2.\sqrt{15}.2\sqrt{3}+\left(2\sqrt{3}\right)^2\right]+12\sqrt{5}\)
\(=\left(15+2.\sqrt{15}.\sqrt{12}+12\right)+12\sqrt{5}\)
\(=15+12\sqrt{5}+12+12\sqrt{5}\)
\(=27+\left(12+12\right)\sqrt{5}\)
\(=27+24\sqrt{5}\)
bài 5 sử dụng hằng đẳng thức bình phương một tổng ( hiệu) để khai phương
a)\(\sqrt{7+4\sqrt{3}}\)
b)\(\sqrt{8-2\sqrt{12}}\)
c)\(\sqrt{21+6\sqrt{6}}\)
d)\(\sqrt{15-6\sqrt{6}}\)
e)\(\sqrt{29-12\sqrt{5}}\)
g)\(\sqrt{41+12\sqrt{5}}\)
1.\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
2.\(\sqrt{9-4\sqrt{5}}-\sqrt{9+\sqrt{80}}\)
3.\(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)
4.\(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)
5.\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)
6.\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
7.\(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
Rút gọn các biểu thức:
1. A=\(\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)\)
2. B= \(\left(\sqrt{45}+\sqrt{63}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
3. C= \(\left(\sqrt{5}+\sqrt{3}\right)\left(5-\sqrt{15}\right)\)
4. D= \(\left(\sqrt{32}-\sqrt{50}+\sqrt{27}\right)\left(\sqrt{27}+\sqrt{50}-\sqrt{32}\right)\)
5. E= \(\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
6. F= \(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)
Tính:
A=\(\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}\)
B=\(\dfrac{1}{\sqrt{3}+2}-\dfrac{1}{\sqrt{3}-2}\)
C=\(\dfrac{3}{\sqrt{3}}+\dfrac{2\sqrt{3}}{\sqrt{3}+1}\)
D=\(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\dfrac{1}{2-\sqrt{3}}\)
rút gọn
a.\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right)\div\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
b.\(\sqrt{2}+\dfrac{1}{\sqrt{5+2\sqrt{6}}}+\dfrac{2}{\sqrt{8+2\sqrt{15}}}\)
Rút gọn:
a)\(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}\)
b)\(\dfrac{6}{\sqrt{5}-1}+\dfrac{7}{1-\sqrt{3}}-\dfrac{2}{\sqrt{3}-\sqrt{5}}\)
c)\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right)\div\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
d)\(\sqrt{2}+\dfrac{1}{\sqrt{5+2\sqrt{6}}}+\dfrac{2}{\sqrt{8+2\sqrt{15}}}\)
e)\(\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\times\left(\sqrt{6}+11\right)\)
Lm nhanh giúp mk nhé, mk đang cần gấp!
Bài 1 : Tính :
a) \(\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}\)
b) \(\sqrt{6+2\sqrt{5}}-\dfrac{\sqrt{15}-\sqrt{3}}{\sqrt{3}}\)
c) \(\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\dfrac{1}{\sqrt{16}}\)
d) \(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{1+\sqrt{2}}-\dfrac{1}{2-\sqrt{3}}\)
e) \(\dfrac{4}{1+\sqrt{3}}-\dfrac{\sqrt{15}+\sqrt{3}}{1+\sqrt{5}}\)
f) \(\left(\dfrac{1}{2-\sqrt{5}}+\dfrac{2}{\sqrt{5}-\sqrt{3}}\right):\dfrac{1}{\sqrt{21-12\sqrt{3}}}\)
Bài 2 : Rút gọn :
a) \(\dfrac{a+b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\dfrac{1}{\sqrt{a}+\sqrt{b}}\)
b) \(\left(\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}}\right).\left(\dfrac{a-\sqrt{a}}{\sqrt{a}+1}-\dfrac{a+\sqrt{a}}{\sqrt{a}-1}\right)\)
c) \(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
BT: Tính
a, \(\frac{5\sqrt{60}.3\sqrt{15}}{15\sqrt{50}.2\sqrt{18}}\)
b, \(\sqrt{27\left(\sqrt{3}-\sqrt{5}\right)^2}\)
c, \(\frac{2-\sqrt{3}}{2\sqrt{6}}\)
d, \(\frac{1}{\sqrt{2}+\sqrt{3}}-\frac{3}{\sqrt{2}-\sqrt{3}}\)
a) \(\sqrt{\left(2\sqrt{6}-4\right)^2}+\sqrt{15-6\sqrt{6}}\)
b) \(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{19+2\sqrt{18}}\)
c) \(\sqrt{9+4\sqrt{5}}-\sqrt{\left(1-\sqrt{5}^2\right)}\)
