\(\sqrt{5^2-4^2}=\sqrt{\left(5-4\right)\left(5+4\right)}=\sqrt{1}.\sqrt{9}=1.3=3\)
\(\sqrt{5^2-4^2}\)
\(\Leftrightarrow\sqrt{25-4^2}\)
\(\Leftrightarrow\sqrt{25-16}\)
\(\Leftrightarrow\sqrt{9}\)
-chúc bạn học tốt-
\(\sqrt{5^2-4^2}=\sqrt{\left(5-4\right)\left(5+4\right)}=\sqrt{1}.\sqrt{9}=1.3=3\)
\(\sqrt{5^2-4^2}\)
\(\Leftrightarrow\sqrt{25-4^2}\)
\(\Leftrightarrow\sqrt{25-16}\)
\(\Leftrightarrow\sqrt{9}\)
-chúc bạn học tốt-
CMR:
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
c) \(23-8\sqrt{7}=\left(4-\sqrt{7}\right)^2\)
d) \(\sqrt{17-12\sqrt{2}}+2\sqrt{2}=3\)
bài 5 Tính:
a) \(\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{7-4\sqrt{3}}\)
c)\(\sqrt{3-2\sqrt{2}}\) -\(\sqrt{6-4\sqrt{2}}\)
d)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
Rút gọn biểu thức
a) \(\sqrt{11-2\sqrt{10}}\)
b) \(\sqrt{9-2\sqrt{14}}\)
c) \(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
d) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
e) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
g) \(\sqrt{3}+\sqrt{11+6\sqrt{2}}+\sqrt{5+2\sqrt{6}}\)
h) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
k) \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
i) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Bài 1: Tính
\(\sqrt{3+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\\ \sqrt{12+6\sqrt{3}+\sqrt{12-6\sqrt{3}}}\\ \sqrt{9-4\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)
\(\sqrt{\sqrt{2}+2+\sqrt{4+\sqrt{9-\sqrt{32}}}}\\ \sqrt{6+2\sqrt{5}-\sqrt{29+12\sqrt{5}}}\\ \sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}-\sqrt{\sqrt{49}+\sqrt{40}}\\ \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
Chứng minh
a) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)
b)\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
Help me plsssssss
Tính
a.\(\sqrt{8+2\sqrt{5}}\) b.\(\sqrt{10-2\sqrt[]{5}}\) c.\(\sqrt{5+\sqrt{24}}\) d.\(\sqrt{12-\sqrt{140}}\)
e.\(\sqrt{14+2\sqrt{5}}\) f. \(\sqrt{8-\sqrt{28}}\) g.\(\sqrt{23-4\sqrt{15}}\) h.\(\sqrt{9+4\sqrt{2}}\)
giúp mik vs mai mik nộp rồi,cảm ơn mn nhiều
tính:
a,\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
b,\(\sqrt{7-4\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
c,\(\dfrac{x-49}{\sqrt{x}-7}\)
d,\(\sqrt{4+2\sqrt{3}}-\sqrt{13+4\sqrt{3}}\)
e,\(2+\sqrt{17-4\sqrt{9+4\sqrt{45}}}\)
Giải các phương trình sau:
a) \(\sqrt{x^2-4+4}=2-x\)
b) \(\sqrt{4x-8}-\dfrac{1}{5}\sqrt{25x-50}=3\sqrt{x-2}-1\)
c) \(\sqrt{x-1}+\sqrt{9x-9}-\sqrt{4x-4}=4\)
d) \(\dfrac{1}{2}\sqrt{x-2}-4\sqrt{\dfrac{4x-8}{9}}+\sqrt{9x-18}-5=0\)
e)\(\sqrt{49-28x+4x^2}-5=0\)
f) \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\sqrt{9x-45}=4\)
g) x2 - 4x - 2\(\sqrt{2x-5}+5=0\)
h)\(\sqrt{3x-2}=\sqrt{x+1}\)
i) x + y + z + 8 = \(2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
k) \(\sqrt{x^2-3x}-\sqrt{x-3}=0\)
l)\(\sqrt{x^2-4}+\sqrt{x-2}=0\)
m) \(4\sqrt{x+1}=x^2-5x+14\)
n) \(\sqrt{x^2-6x+9}-\sqrt{4x^2+4x+1}=0\)
1)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
2)\(\sqrt{35+12\sqrt{6}}-\sqrt{35-12\sqrt{6}}\)
3)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
Tính và rút gọn :
1) \(\sqrt{36+12\sqrt{5}}\)
2) \(\sqrt{21-6\sqrt{6}}\)
3) \(\sqrt{6-2\sqrt{5}}\)\(\:-\sqrt{9-4\sqrt{5}}\)
4) \(\sqrt{3+2\sqrt{2}}\)\(-\sqrt{3-2\sqrt{2}}\)
5) \(\sqrt{4-2\sqrt{3}}\) \(-\sqrt{4+2\sqrt{3}}\)
6) \(\sqrt{6+4\sqrt{2}}\) \(-\sqrt{11-6\sqrt{2}}\)
7) \(\sqrt{21-4\sqrt{5}}\) \(+\sqrt{21+4\sqrt{5}}\)