\(B=\left(2+\sqrt{3}\right)^3\left(2-\sqrt{3}\right)^3=\left[\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\right]^3=\left[2^2-\left(\sqrt{3}\right)^2\right]^3=\left(4-3\right)^3=1^3=1\)Vậy B=1
a,\(\left(4\sqrt{3}+2\sqrt{5}\right)\sqrt{3}-\sqrt{60}\)
b,\(\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}\)
tính
1.\(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)
2.\(3\sqrt{2}\left(4-\sqrt{2}\right)+3\left(1-2\sqrt{2}\right)^2\)
3.\(\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)
4.\(\left(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\right)^2\)
5.\(\left(\sqrt{\sqrt{14}+\sqrt{5}}+\sqrt{\sqrt{14}-\sqrt{5}}\right)^2\)
6.\(\left(\sqrt{3}+1\right)^3-\left(\sqrt{3}-1\right)^3\)
7.\(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
8.\(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
9.\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
Bài 1: Rút gọn căn bậc 2 theo hằng đẳng thức 1:
a)\(\sqrt{\left(23-15\sqrt{3}\right)^2}\)
b) \(\sqrt{\left(2-2\sqrt{3}\right)^2}\)
c) \(\sqrt{\left(15-4\sqrt{3}\right)^2}\)
d)\(\sqrt{\left(16-6\sqrt{7}\right)^2}\)
f)\(\sqrt{\left(22-8\sqrt{3}\right)^2}\)
g) \(\sqrt{\left(9-4\sqrt{2}\right)^2}\)
h) \(\sqrt{\left(13-4\sqrt{3}\right)^2}\)
i)\(\sqrt{\left(7-3\sqrt{3}\right)^2}\)
(mink đag cần gấp)
thực hiện phép tính
a)\(\dfrac{\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}\)
b)\(\dfrac{\left(\sqrt{5}-1\right)^3}{\sqrt{5}-2}\)
c)\(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
d)\(\dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{2}}-\dfrac{\sqrt{5}-1}{2}\)
\(\frac{x+3+2\left(\sqrt{x-3}\right)+\left(\sqrt{x+3}\right)}{\left(\sqrt{x+3}\right)\left(\sqrt{x-3}\right)}\)
Tính :
a) \(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\)
b) \(\dfrac{3\sqrt{8}-2\sqrt{12}+\sqrt{40}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
\(5\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\dfrac{5}{2}}\right)^2+\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\dfrac{3}{2}}\right)^2\)
\(21\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}\right)^2-6\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}\right)^2-15\sqrt{15}\)
C1. Tính:
a) \(\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)
b) \(\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)
C2. Tính
P = \(\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\) , \(a\ge0,b\ge0,a\ne b\)
Giải phương trình:
a. \(\left(\sqrt{3}-1\right)x=2\left(\sqrt{3}+1\right)x-3\sqrt{3}\)
b. \(\left(\sqrt{3}-1\right)x-x+4-2\sqrt{3}=0\)
