Em coi lại đề, biểu thức này muốn rút gọn thì con số kia cần phải là những con số như 24 hoặc 21 hoặc 81... tức là dạng \(\sqrt{21+8\sqrt{5}}\) hoặc \(\sqrt{24+8\sqrt{5}}\), chứ \(\sqrt{25+8\sqrt{5}}\) thì ko rút được
Chứng minh rằng:
a)\(\left(\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\right)^8>3^6\)
b) \(\sqrt[3]{\sqrt[5]{\frac{32}{5}}-\sqrt[5]{\frac{27}{5}}}=\sqrt[5]{\frac{1}{25}}+\sqrt[5]{\frac{3}{25}}-\sqrt[5]{\frac{9}{25}}\)
giải phương trình:
1,\(\sqrt{3x-8}\)-\(\sqrt{x+1}\)=\(\dfrac{2x-11}{5}\)
2,3x2-3x+18=10\(\sqrt{x^3+8}\)
3,\(\sqrt{5+2x}\)+\(\sqrt{5-2x}\)+5=3\(\sqrt{25-4x^2}\)
rút gọn biểu thức
A=2015+\(\sqrt{36}\)-\(\sqrt{25}\)
B=5\(\sqrt{8}\)+\(\sqrt{50}\)-2\(\sqrt{18}\)
C=\(\sqrt{27}\)-2\(\sqrt{12}\)-\(\sqrt{75}\)
D=\(\sqrt{12}\)+\(\sqrt{27}\)-\(\sqrt{48}\)
Rút gọn biểu thức
I=(2\(\sqrt{3}\)-5\(\sqrt{27}\)+4\(\sqrt{12}\)):\(\sqrt{3}\)
K=\(\sqrt{125}\)-4\(\sqrt{45}\)+3\(\sqrt{20}\)-\(\sqrt{80}\)
L=2\(\sqrt{9}\)+\(\sqrt{25}\)-5\(\sqrt{4}\)
N=2\(\sqrt{32}\)-5\(\sqrt{27}\)-4\(\sqrt{8}\)+3\(\sqrt{75}\)
O=2\(\sqrt{3.5^2}\)-3\(\sqrt{3.2^2}\)+\(\sqrt{3.3^2}\)
\(\left(\sqrt{8-\sqrt{X-3}}-\sqrt{5-\sqrt{X-3}}\right)^2=5^2\)=\(5^2\)
\(\Leftrightarrow-2\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}=25-3=22\)
\(\Leftrightarrow-\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}=11\)
Do \(\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}\ge0\Rightarrow-\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}\le0\)
\(\Rightarrow\)PT vô nghiệm
Thực hiện phép tính:
\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
\(\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)\)
\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
a/ \(\frac{\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
b/ \(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
c/ \(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
d/ \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
e/ \(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
Làm ơn, giúp mik với. Mik đang cần gấp lắm!
Tìm điều kiện có nghĩa:
1) \(\sqrt{2x^2}\)
2) \(\sqrt{-x}\)
3) \(\sqrt{-x^2-3}\)
4) \(\sqrt{x^2+2x+3}\)
5) \(\sqrt{-a^2+8a-16}\)
6) \(\sqrt[]{16x^2-25}\)
7) \(\sqrt{4x^2-49}\)
8) \(\sqrt{8-x^2}\)
9) \(\sqrt{x^2-12}\)
10) \(\sqrt{x^2+2x-3}\)
11) \(\sqrt{2x^2+5x+3}\)
12) \(\sqrt{\dfrac{4}{x-1}}\)
13) \(\sqrt{\dfrac{-1}{x-3}}\)
14) \(\sqrt{\dfrac{-3}{x+2}}\)
15) \(\sqrt{\dfrac{1}{2a-1}}\)
16) \(\sqrt{\dfrac{2}{3-2a}}\)
17) \(\sqrt{\dfrac{-1}{2a-5}}\)
18) \(\sqrt{\dfrac{-2}{3-5a}}\)
19) \(\sqrt{\dfrac{-a}{5}}\)
20) \(\dfrac{1}{\sqrt{-3a}}\)
a) \(\dfrac{2}{5}\sqrt{25}\) -\(\dfrac{1}{2}\sqrt{4}\) b)0,5\(\sqrt{0,09}\) +5\(\sqrt{0,81}\) c)\(\dfrac{2}{5}\sqrt{\dfrac{25}{36}}\) -\(\dfrac{5}{2}\sqrt{\dfrac{4}{25}}\)
d)-2\(\sqrt{\dfrac{-36}{-16}}\) + 5\(\sqrt{\dfrac{-81}{-25}}\)
