a) \(\sqrt{49}+\sqrt{25}-4\cdot0,25\)
\(=7+5-1=11\)
b) \(\sqrt{\frac{1}{9}}\cdot\sqrt{0,81}\cdot\sqrt{0,9}\)
\(=\frac{1}{3}\cdot\frac{9}{10}\cdot\frac{3\sqrt{10}}{10}\)
\(=\frac{9\sqrt{10}}{100}\)
c) \(\sqrt{6,4\cdot2400\cdot0,6}\)
\(=\sqrt{64\cdot36\cdot4}\)
\(=8\cdot6\cdot2=96\)
d) \(\sqrt{26^2-24^2}=\sqrt{\left(26-24\right)\left(26+24\right)}\)
\(=\sqrt{2\cdot50}=\sqrt{100}=10\)
Thực hiện các phép tính sau:
a, \(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-2\right)\cdot\sqrt{\sqrt{3}+2}\)
b, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
c, \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
d, \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\)
Tìm các giá trị của x để căn thức sau có nghĩa:
a) \(\sqrt{4-5x}\)
b) \(\sqrt{\frac{x^2+1}{x-3}}\)
c) \(\sqrt{\frac{x-1}{x^2+2}}\)
d) \(\sqrt{\frac{2x-3}{x-1}}\)
e) \(\frac{\sqrt{2x-3}}{\sqrt{x-1}}\)
2/ Thực hiện phép tính:
a) \(\sqrt{\frac{16}{64}\cdot\frac{144}{9}\cdot\frac{25}{196}}\)
b) \(\left(\sqrt{8}+5\sqrt{2}-\sqrt{20}\right)\sqrt{5}-7\sqrt{10}\)
Chứng minh: \(\frac{1}{2\cdot\sqrt{1}}+\frac{1}{3\cdot\sqrt{2}}+\frac{1}{4\cdot\sqrt{3}}+...+\frac{1}{2012\cdot\sqrt{2011}}+\frac{1}{2013\cdot\sqrt{2012}}\)\(< 2\)
Chứng minh: A=\(\frac{1}{3\cdot\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\cdot\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\cdot\left(\sqrt{48}+\sqrt{49}\right)}\)\(< \frac{1}{2}\)
Thực hiện phép tính:\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2-\sqrt{2+\sqrt{3}}}\)
1. CHỨNG MINH ĐẲNG THỨC
a. \(\text{[}3+2\sqrt{6}-\sqrt{33}\text{]}\cdot\text{[}\sqrt{22}+\sqrt{6}+4\text{]}=24\)
b. \(\text{[}\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\text{]}\cdot\text{[}15+2\sqrt{6}\text{]}\)
c.\(\text{[}\frac{4}{3}\cdot\sqrt{3}+\sqrt{2}+\sqrt{3\frac{1}{3}}\text{]}\cdot\text{[}\sqrt{1,2}+\sqrt{2}-4\sqrt{\frac{1}{5}}\text{]}=4\)
d. \(\sqrt{\text{[}1-\sqrt{1989}\text{]}^2}\cdot\sqrt{1990+2\sqrt{1989}}=1988\)
e. \(\frac{a-\sqrt{ab}+b}{a\sqrt{a}+b\sqrt{b}}-\frac{1}{a-b}=\frac{\sqrt{a}-\sqrt{b}-1}{a-b}\)với \(a>0;b>0\)và \(a\ne b\)
\(\frac{\left(5+\sqrt{24}\right)\cdot\left(49-20\sqrt{6}\right)\cdot\sqrt{5-2\sqrt{6}}}{9\sqrt{30}-11\sqrt{2}}\)
Tính ghi rõ cách giải
Bài 1. thực hiện phép tính
a) \(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\) b) \(\sqrt{\frac{4+\sqrt{7}}{4-\sqrt{7}}}+\sqrt{\frac{4-\sqrt{7}}{4+\sqrt{7}}}\)
Bài 2. Tính:a) \(M=\left(2\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+\sqrt{11-6\sqrt{2}}}}\)
b) \(\frac{1}{\sqrt{25}+\sqrt{24}}+\frac{1}{\sqrt{24}+\sqrt{23}}+...+\frac{1}{\sqrt{2}+\sqrt{1}}=4\)
c)
\(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}0-5\sqrt{2}}\)
Thực hiện các phép tính sau:
a, \(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
b, \(\sqrt{21-12\sqrt{3}}-\sqrt{3}\)
c, \(\left(\sqrt{6}+\sqrt{2}\right)\cdot\left(\sqrt{3}-2\right)\sqrt{\sqrt{3}+2}\)
d, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
e, \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)\
f, \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18}-\sqrt{128}}}\)
Thực hiện phép tính:
a, M = \(\sqrt{9+4\sqrt{5}}\) - \(\sqrt{9-4\sqrt{5}}\)
b, N = \(\sqrt{8-2\sqrt{7}}\) - \(\sqrt{8+2\sqrt{7}}\)
