\(\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{72}\)
\(=3-\sqrt{2}+6\sqrt{2}\)
\(=5\sqrt{2}+3\)
= \(3-\sqrt{2}+6\sqrt{2}\)
= \(5\sqrt{2}+3\)
a, \(\sqrt{200}-\sqrt{32}+\sqrt{72}\)
b, \(4\sqrt{20}-3\sqrt{125}+5\sqrt{45}-15\sqrt{\dfrac{1}{5}}\)
c, \(\left(2\sqrt{8}+3\sqrt{5}-7\sqrt{2}\right)\left(72-5\sqrt{20}-2\sqrt{2}\right)\)
\(\left(4\sqrt{8}-\sqrt{72}+5\sqrt{\dfrac{1}{2}}\right)2\sqrt{2}\)
\(\dfrac{5+\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}+1}\left(\sqrt{3}+\sqrt{5}\right)\)
Rút gọn các biểu thức sau
a) 2\(\sqrt{32}\) + 3\(\sqrt{72}-7\sqrt{50}+\sqrt{2}\) b)\(\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{\left(2-\sqrt{3}\right)^2}\) c) \(\sqrt{11+6\sqrt{2}}-3+\sqrt{2}\)
d) \(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\) e) \(\dfrac{1}{a-b}\sqrt{a^4\left(a-b\right)^2}vớia< b\)
Tính:
\(a)D=\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\left(-\sqrt{2}\right)\\ b)2\sqrt{3}\left(\sqrt{27}+2\sqrt{48}\right)-\sqrt{75}\\ c)E=\left(\sqrt{10}+\sqrt{6}\right)\sqrt{8-2\sqrt{15}}\\ d)P=\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
\(e)M=-3\sqrt{50}+2\sqrt{98}-7\sqrt{72}\)
Tính
a) \(\left(\sqrt{8}+\sqrt{72}-\sqrt{2}\right).\sqrt{2}\)
b) \(\left(\sqrt{5}+\sqrt{2}+1\right).\left(\sqrt{5}-1\right)\)
c) \(\left(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\right)^2\)
d) \(\left(\sqrt{2}+1+\sqrt{3}\right).\left(\sqrt{2}+1-\sqrt{3}\right)\)
e)\(\left(\sqrt{\frac{9}{2}}+\sqrt{\frac{1}{2}}-\sqrt{2}\right).\sqrt{2}\)
f) \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
1. làm tính nhân :
a) \(\left(\sqrt{12}-3\sqrt{75}\right).\sqrt{3}\)
b) \(\left(\sqrt{18}-4\sqrt{72}\right).2\sqrt{2}\)
c) \(\left(\sqrt{6}-2\right)\left(\sqrt{6}+7\right)\)
d) \(\left(\sqrt{3}+2\right)\left(\sqrt{3}-5\right)\)
a
\(\sqrt{32}\)+\(\sqrt{50}\) - 2\(\sqrt{200}\) + 3\(\sqrt{72}\)
b)\(\dfrac{3}{\sqrt{ }2-1}\) + \(\sqrt{\left(3-\sqrt{2}\right)^{^2}}\) - 2\(\sqrt{2}\)
rút gọn các biểu thức trên
cmr\(\frac{1}{\left(\sqrt{2}+\sqrt{5}\right)^3}+\frac{1}{\left(\sqrt{5}+\sqrt{8}\right)^3}+...+\frac{1}{\left(\sqrt{32+\sqrt{35}}\right)^3}<\frac{5}{72}\)
Rút gọn
a)\(\frac{1}{2}\sqrt{12}+3\sqrt{\frac{1}{2}}+\)\(2\sqrt{3}\)
b)\(\sqrt{45}-2\sqrt{18}+\sqrt{20}-3\sqrt{72}\)
c)\(\left(3+\sqrt{3}\right).2\sqrt{3}-\left(2\sqrt{3}-4\right)^2\)
d)\(\left(\sqrt{7}-\sqrt{28}+2\sqrt{3}\right).\sqrt{7}+\sqrt{84}\)
e)\(\left(\sqrt{2}+\sqrt{3}\right)^2-\sqrt{96}\)
