\(\text{ĐKXĐ: }x\ge0;x\ne\pm1\)
\(2\sqrt{144x+144}-3\sqrt{100x-100}=12\)
\(2\sqrt{144\left(x+1\right)}-3\sqrt{100\left(x-1\right)}=12\)
\(2\sqrt{144}.\sqrt{\left(x+1\right)}-3\sqrt{100}.\sqrt{x-1}=12\)
\(2.12\sqrt{x+1}-3.10\sqrt{x-1}=12\)
\(24\sqrt{x+1}-30\sqrt{x-1}=12\)
\(6.\left(4\sqrt{x+1}-5\sqrt{x-1}\right)=6.2\)
\(4\sqrt{x+1}-5\sqrt{x-1}=2\)
\(\text{Mk bí r}\)
Tính
\(\frac{1-\sqrt{2}}{\sqrt{2}}+\frac{\sqrt{2}-\sqrt{3}}{\sqrt{6}}+\frac{\sqrt{3}-\sqrt{4}}{\sqrt{12}}+...+\frac{\sqrt{99}-\sqrt{100}}{\sqrt{9900}}\)
Rút gọn biểu thức sau
A=\(\dfrac{1}{x-1}\sqrt{75\left(x-1\right)^3}\left(x>1\right)
\)
B=\(5\sqrt{4x}-3\sqrt{\dfrac{100x}{9}}-\dfrac{4}{x}\sqrt{\dfrac{x^3}{4}}\left(x>0\right)
\)
C=\(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\)
Help me
Tính giá trị
a) A= \(\sqrt{49}\)- 2\(\sqrt{36}\) + 3\(\sqrt{4}\)
b) B= \(\frac{1}{2}\)\(\sqrt{\frac{144}{225}}\)- 7\(\sqrt{100}\)+4\(\sqrt{\frac{361}{400}}\)
rút gọn và tính biểu thức sau
a, \(3\sqrt{144}-5\sqrt{49}+\dfrac{1}{2}\sqrt{36}\)
Tính:
a, \(\sqrt{49}\) . \(\sqrt{144}\) + \(\sqrt{256}\) : \(\sqrt{64}\)
b, 72 : \(\sqrt{2^2.36.3^2}\) - \(\sqrt{225}\)
Rút gọn biểu thức
1) \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8+2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
2) \(\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right):\left(\sqrt{5}-2\right)\)
3) \(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
4) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
5) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...-\frac{1}{\sqrt{98}-\sqrt{99}}+\frac{1}{\sqrt{99}-\sqrt{100}}\)
6) \(\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
7)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)
\(\sqrt{3}-\sqrt{27}-\sqrt{144}:\sqrt{36}\)
tính:
a/\(\frac{6}{4+\sqrt{4-2\sqrt{3}}}\)
b/\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
c/\(\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{4}+\sqrt{3}}+....+\frac{1}{\sqrt{100}-\sqrt{99}}\)
d/\(\frac{1}{\sqrt{7-2\sqrt{10}}}+\frac{1}{\sqrt{7+2\sqrt{10}}}\)
x=\(\dfrac{7}{\sqrt[3]{26+15\sqrt{3}}}-\sqrt{26+15\sqrt{3}}\)
Tính Q=\(\dfrac{x^6+x^4+4x^2}{40\left(x^4+4x^2-144\right)}\)
