\(\sqrt{5\sqrt{3}}=\sqrt{\sqrt{75}}>\sqrt{\sqrt{45}}=\sqrt{3\sqrt{5}}\)
`sqrt(5sqrt 3)) = sqrt(sqrt 75)`.
`sqrt(3 sqrt 5) = sqrt(sqrt45)`.
`-> sqrt(5sqrt3) > sqrt(3sqrt 5)`
Không dùng máy tính ,hãy so sánh :
1 )\(\sqrt{7-\sqrt{21}+4\sqrt{5}}v\text{à}\sqrt{5}-1\)
2 )\(\sqrt{5}+\sqrt{10}+1v\text{à}\sqrt{35}.\)
3 )\(\frac{15-2\sqrt{10}}{3}v\text{à}\sqrt{15}.\)
So Sánh Các Biểu Thức Sau:
a,\(\sqrt{2}+\sqrt{11}v\text{à}\sqrt{3}+4\) 4
b, \(\sqrt{21}-\sqrt{5}v\text{à}\)\(\sqrt{20}-\sqrt{6}\)
c,\(\sqrt{24}-1v\text{à}\)\(5\)
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 \(a\ne b\)
so sánh\(\sqrt[3]{\left(1-\sqrt{3}\right)\left(4-2\sqrt{3}\right)}v\text{à}\sqrt[3]{\left(1-\sqrt{5}\right)\left(6-2\sqrt{5}\right)}\)
Mọi người ơi giúp mk vs ạ mk đag cần gấp!
câu 1 Tìm x biết
a)\(\sqrt{2\text{x}-1}=\sqrt{5}\)
b)\(\sqrt{x-10}=-2\)
c)\(\sqrt{\left(x-5\right)}=3\)
Thực Hiện Phép Tính Sau :
\(\text{a)}\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
\(\text{b)}\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
\(\text{c)}\sqrt{1+\sqrt{3+\sqrt{13+4\sqrt{3}}}}+\sqrt{1-\sqrt{3-\sqrt{13-4\sqrt{3}}}}\)
Ai giúp mk vs. Mk tick cho
giải phương trình:
\(\sqrt{3\text{x}^{2^{ }}-5\text{x}+1}-\sqrt{\text{x}^2-2}=\sqrt{3\left(\text{x}^2-\text{x}-1\right)}-\sqrt{\text{x}^{2^{ }}-3\text{x}+4}\)
Rút gọn: \(\frac{\sqrt{1+2\sqrt{5\sqrt{\text{7}}-13}}-\sqrt{\sqrt{\text{7}}-2}}{\sqrt{3}-\sqrt{\text{7}}}-\sqrt{\frac{2}{3-\sqrt{5}}}\)
\(\sqrt{\text{x}}\) = \(\dfrac{\text{5}}{\sqrt{\text{x}}+2}\)
Tìm \(x\)
Giúp e với;-;
Bài 1 Rút gọn và tính
a, \(\sqrt{\frac{\sqrt{a}-1}{\sqrt{b}+1}}:\sqrt{\frac{\sqrt{b}-1}{\sqrt{a}+1}}\)với a=7.25;b=3.25
b,\(\sqrt{15\text{a}^2-8\text{a}\sqrt{15}+16}\) với \(a=\sqrt{\frac{3}{5}}+\sqrt{\frac{5}{3}}\)
c,\(\sqrt{10\text{a}^2-4\text{a}\sqrt{10}+4}\)với \(a=\sqrt{\frac{2}{5}}+\sqrt{\frac{5}{2}}\)
d,\(\sqrt{a^2+2\text{a}\sqrt{a^2-1}}-\sqrt{a^2-2\sqrt{a^2-1}}v\text{ới}\)\(a=\sqrt{5}\)
