\(\sqrt{6}+\sqrt{15}+\sqrt{21}\)
\(=\sqrt{3}\cdot\sqrt{2}+\sqrt{3}\cdot\sqrt{5}+\sqrt{3}\cdot\sqrt{7}\)
\(=\sqrt{3}\cdot\left(\sqrt{2}+\sqrt{5}+\sqrt{7}\right)\)
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.Giá trị biểu thức
\(\sqrt{15-6\sqrt{6}}\) + \(\sqrt{15+6\sqrt{6}}\) bằng
A. 3
B. 12\(\sqrt{6}\)
C. \(\sqrt{30}\)
D. 6
2.Biểu thức \(\sqrt{2}.\sqrt{8}\) có giá trị là :
A. 4
B. một kết quả khác
C. 16
D. -4
3. Giá trị của \(\sqrt{\sqrt{16}}\) bằng :
A. 16
B. 4
C. 2
D. 8
4. Biểu Thức \(\sqrt{-2x+3}\) có nghĩa khi:
A. x ≥ \(\dfrac{2}{3}\)
B. x ≤ \(\dfrac{3}{2}\)
C. x ≥ \(\dfrac{3}{2}\)
D. x ≤ \(\dfrac{2}{3}\)
5.\(\sqrt{^{\left(2x+1\right)^2}}\) bằng:
A. |2x+1|
B. -(2x+1)
C. |-2x+1|
D. 2x+1
Tính :
a) \(\dfrac{5+2\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}}-\left(\sqrt{5}+\sqrt{3}\right)\)
b) \(\left(\dfrac{1}{2-\sqrt{5}}+\dfrac{2}{\sqrt{5}+\sqrt{3}}\right):\dfrac{1}{\sqrt{21+12\sqrt{3}}}\)
c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}\)
d) \(\sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
e) \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
f) \(\dfrac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(\sqrt{5-2\sqrt{6}}\right)}{9\sqrt{3}-11\sqrt{2}}\)
g) \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)-\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-a\right)^2}\)
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) \(\sqrt{9+4\sqrt{5}}-\sqrt{\left(1-\sqrt{5}^2\right)}\)
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
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.\(\sqrt{2}+\dfrac{1}{\sqrt{5+2\sqrt{6}}}+\dfrac{2}{\sqrt{8+2\sqrt{15}}}\)
\(\sqrt{8-2\sqrt{15}}+\sqrt{48+6\sqrt{15}}\)
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) \(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
Bài 1:
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) \(\sqrt{9+4\sqrt{5}}-\sqrt{\left(1-\sqrt{5}^2\right)}\)
Bài 2: Biến đổi biểu thức
a) \(\dfrac{1}{\sqrt{7}+3}+\dfrac{1}{\sqrt{7}-3}\)
b) \(\dfrac{3}{\sqrt{2}-1}+\dfrac{\sqrt{6}+\sqrt{2}}{\sqrt{3}+1}\)
c) \(\dfrac{1}{7+4\sqrt{3}}+\dfrac{1}{7-4\sqrt{3}}\)
