\(P=\dfrac{3a-12\sqrt{a}+a+4\sqrt{a}-4a-8}{\left(\sqrt{a}+4\right)\left(\sqrt{a}-4\right)}:\dfrac{\sqrt{a}+4-2\sqrt{a}-5}{\left(\sqrt{a}+4\right)}\)
\(=\dfrac{-8\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+4\right)\left(\sqrt{a}-4\right)}\cdot\dfrac{\sqrt{a}+4}{-\left(\sqrt{a}+1\right)}=\dfrac{8}{\sqrt{a}-4}\)
rút gọn biểu thức sau
P=(\(\frac{3\sqrt{a}}{\sqrt{a}+4}+\frac{\sqrt{a}}{\sqrt{a}-4}+\frac{4\left(a+2\right)}{16-a}\))\(:\left(1-\frac{2\sqrt{a}+5}{\sqrt{a}-4}\right)\)
Rút gọn biểu thức
a)\(\frac{a-1}{\sqrt[3]{a^2}+\sqrt[3]{a}+1}\)\
b)\(\left(12\sqrt[3]{2}+\sqrt[3]{16}-2\sqrt[3]{2}\right)\left(5\sqrt[3]{4}-3\sqrt[3]{\frac{1}{2}}\right)\)
Rút gọn biểu thức :
\(\frac{\sqrt{7-4\sqrt{3}}}{\sqrt{2-\sqrt{3}}}.\sqrt{2+\sqrt{3}}\)
\(\left[\left(a-b\right)\sqrt{\frac{a+b}{a-b}}+a-b\right]\left(a-b\right)\left(\sqrt{\frac{a+b}{a-b}}-1\right)\)với a>b>0
Chứng minh rằng :
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=2\)
GIúp mình với
Rút gọn các biểu thức sau :
a)\(\left[\left(a-b\right)\sqrt{\frac{a+b}{a-b}}+a-b\right]\left(a-b\right)\left(\sqrt{\frac{a+b}{a-b}}-1\right)\)với a > b > 0
b)\(\frac{\sqrt{7-4\sqrt{3}}}{\sqrt{2-\sqrt{3}}}.\sqrt{2+\sqrt{3}}\)
Chứng minh rằng
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=2\)
K= \(\left(\frac{\sqrt{a}}{\sqrt{a}-2}+\frac{\sqrt{2}}{\sqrt{a}+2}\right):\frac{\sqrt{4a}}{a-4}\)
(a#4; a>0)
Rút gọn
cho biểu thức \(P=\left(\frac{1}{1-\sqrt{a}}-\frac{1}{\sqrt{a}}\right):\left(\frac{2a+\sqrt{a}-1}{1-a}+\frac{2a\sqrt{a}+a-\sqrt{a}}{1+a\sqrt{a}}\right)\)
a. rút gọn P KQ=\(\frac{1-\sqrt{a}+a}{\sqrt{a}}\)
b. tính P khi \(a=\frac{\sqrt{3+\sqrt{5}}\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{10}+\sqrt{2}\right)\left(3-\sqrt{5}\right)}{2\sqrt{3+\sqrt{5-\sqrt{13-\sqrt{48}}}}}+1\) KQ =7/3
c. tìm x để P>x
lm hooj t câu c vs câu a,b, t lm hết r
1 Tính
a) \(\sqrt{0.9\times0.16\times0.4}\)
b) \(\sqrt{0,0016}\)
c)\(\frac{\sqrt{72}}{\sqrt{2}}\)
d) \(\frac{\sqrt{2}}{\sqrt{288}}\)
2 Rút gọn
a) \(\frac{2}{a}.\sqrt{\frac{16a^2}{9}}\left(a< 0\right)\)
b) \(\frac{3}{a-1}.\sqrt{\frac{4a^2-8a+4}{25}}\left(a>1\right)\)
c) \(\frac{\sqrt{243a}}{\sqrt{3a}}\left(a>0\right)\)
d) \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}\left(a\ne0,b\ne0\right)\)
\(Q=\left(\frac{4\sqrt{x}}{2+\sqrt{x}}+\frac{8x}{4-x}\right):\left(\frac{\sqrt{x}-1}{x-2\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)
a. Rút gọn Q
b. Tìm x để Q = -1
Kamsamita. Saranghaeyo
rút gọn P: P=\(\left(\frac{a+\sqrt{a^2-b^2}}{a-\sqrt{a^2}-b^2}-\frac{a-\sqrt{a^2-b^2}}{a+\sqrt{a^2-b^2}}\right):\frac{4\sqrt{a^4-a^2b^2}}{b^2}\)
