Tính giá trị biểu thức: \(\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}\)
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NV
Nguyễn Việt Lâm
Giáo viên
1 tháng 8 2021
\(\sqrt{7+4\sqrt{3}}=\sqrt{\left(2+\sqrt{3}\right)^2}=2+\sqrt{3}\)
\(\sqrt{8-2\sqrt{12}}=\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}=\left|\sqrt{6}-\sqrt{2}\right|=\sqrt{6}-\sqrt{2}\)
\(\sqrt{21+6\sqrt{6}}=\sqrt{\left(3\sqrt{2}-\sqrt{3}\right)^2}=\left|3\sqrt{2}-\sqrt{3}\right|=3\sqrt{2}-\sqrt{3}\)
\(\sqrt{15-6\sqrt{6}}=\sqrt{\left(3-\sqrt{6}\right)^2}=\left|3-\sqrt{6}\right|=3-\sqrt{6}\)
\(\sqrt{29-12\sqrt{5}}=\sqrt{\left(2\sqrt{5}-3\right)^2}=\left|2\sqrt{5}-3\right|=2\sqrt{5}-3\)
\(\sqrt{41+12\sqrt{5}}=\sqrt{\left(6+\sqrt{5}\right)^2}=6+\sqrt{5}\)
P
0
P
1
AH
Akai Haruma
Giáo viên
5 tháng 7 2020
Lời giải:
\(\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}=\sqrt{6^2+5-2.6\sqrt{5}}-\sqrt{6^2+5+2.6\sqrt{5}}\)
\(=\sqrt{(6-\sqrt{5})^2}-\sqrt{(6+\sqrt{5})^2}=|6-\sqrt{5}|-|6+\sqrt{5}|\)
\(=(6-\sqrt{5})-(6+\sqrt{5})=-2\sqrt{5}\)
L
1
4 tháng 9 2023
\(\sqrt{28-10\sqrt{3}}\\ =\sqrt{3-10\sqrt{3}+25}\\ =\sqrt{\left(\sqrt{3}-5\right)^2}\\ =\left|\sqrt{3}-5\right|\\ =5-\sqrt{3}\)
\(\sqrt{41+12\sqrt{5}}\\ =\sqrt{5+12\sqrt{5}+36}\\ =\sqrt{\left(\sqrt{5}+6\right)}\\ =\left|\sqrt{5}+6\right|\\ =\sqrt{5}+6\)
\(\sqrt{32-10\sqrt{7}}\\ =\sqrt{7-10\sqrt{7}+25}\\ =\sqrt{\left(\sqrt{7}-5\right)^2}\\ =\left|\sqrt{7}-5\right|\\ =5-\sqrt{7}\)
\(\sqrt{11-4\sqrt{7}}\\ =\sqrt{7-4\sqrt{7}+4}\\ =\sqrt{\left(\sqrt{7}-2\right)^2}=\left|\sqrt{7}-2\right|\\ =\sqrt{7}-2\)
4 tháng 9 2020
Bài 1:
a) \(=5.|2a|-5a^2\)
b) \(=7\left(a-1\right)+5a=12a-7\)
c) \(|a-2|-5\sqrt{a+2}\)
Bài 2:
a) \(=3-\sqrt{2}+5-\sqrt{2}=8-2\sqrt{2}\)
b) \(=3+\sqrt{2}-\left(3-\sqrt{2}\right)\)
\(=2\sqrt{2}\)
c) \(=6-\sqrt{5}-\left(6+\sqrt{5}\right)\)
\(=-2\sqrt{5}\)
TT
5 tháng 9 2020
a) \(5\sqrt{4a^2}-5a^2\)
\(=5.|2a|-5a^2\)
b) \(7\sqrt{\left(a-1\right)^2}+5a\)
\(=7\left(a-1\right)+5a\)
\(=12a-7\)
c) \(\sqrt{\left(2-a\right)^2}-5\sqrt{a+2}\)
\(=|a-2|-5\sqrt{a+2}\)
bài 2:
a)\(\sqrt{\left(3-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}-5\right)^2}\)
\(=3-\sqrt{2}+5-\sqrt{2}\)
\(=8-2\sqrt{2}\)
b) \(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(=3+\sqrt{2}-\left(3-\sqrt{2}\right)\)
\(=2\sqrt{2}\)
c)\(\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}\)
\(=6-\sqrt{5}-\left(6+\sqrt{5}\right)\)
\(=-2\sqrt{5}\)
TH
0
H9
HT.Phong (9A5)
CTVHS
11 tháng 10 2023
1) \(A=3\sqrt{\dfrac{1}{3}}-\dfrac{5}{2}\sqrt{12}-\sqrt{48}\)
\(=3\cdot\dfrac{\sqrt{1}}{\sqrt{3}}-\dfrac{5\sqrt{12}}{2}-\sqrt{4^2\cdot3}\)
\(=\dfrac{3\cdot1}{\sqrt{3}}-\dfrac{5\cdot2\sqrt{3}}{2}-4\sqrt{3}\)
\(=\sqrt{3}-5\sqrt{3}-4\sqrt{3}\)
\(=-8\sqrt{3}\)
2) \(A=\sqrt{12-4x}\) có nghĩa khi:
\(12-4x\ge0\)
\(\Leftrightarrow4x\le12\)
\(\Leftrightarrow x\le\dfrac{12}{4}\)
\(\Leftrightarrow x\le3\)
3) \(\dfrac{2x-2\sqrt{x}}{x-1}\)
\(=\dfrac{2\sqrt{x}\cdot\sqrt{x}-2\sqrt{x}}{\left(\sqrt{x}\right)^2-1^2}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{2\sqrt{\text{x}}}{\sqrt{x}+1}\)
\(\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}\)
\(=\sqrt{41-2.6\sqrt{5}}-\sqrt{41+2.6\sqrt{5}}\)
\(=\sqrt{36-2.6\sqrt{5}+5}-\sqrt{36+2.6\sqrt{5}+5}\)
\(=\sqrt{\left(6-\sqrt{5}\right)^2}-\sqrt{\left(6+\sqrt{5}\right)^2}\)
\(=\left|6-\sqrt{5}\right|-\left|6+\sqrt{5}\right|=6-\sqrt{5}-6-\sqrt{5}=-2\sqrt{5}\)
\(\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}\)
\(\sqrt{\left(6-\sqrt{5}\right)^2}-\sqrt{\left(6+\sqrt{5}\right)^2}\)
\(\left|6-\sqrt{5}\right|\left|6+\sqrt{5}\right|\)
\(6-\sqrt{5}-6-\sqrt{5}\)
\(2\sqrt{5}\)