Rút gọn đa thức đơn giản chứa căn
\(2\sqrt{32}-5\sqrt{27}-4\sqrt{8}+3\sqrt{75}\)
K
Khách
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Những câu hỏi liên quan
Y
22 tháng 6 2023
\(I=\left(2\sqrt{3}-5\sqrt{27}+4\sqrt{12}\right):\sqrt{3}\)
\(=\left(2\sqrt{3}-5\sqrt{3}.\sqrt{3^2}+2\sqrt{2^2}.\sqrt{3}\right):\sqrt{3}\)
\(=\left(2\sqrt{3}-15\sqrt{3}+8\sqrt{3}\right):\sqrt{3}\)
\(=-5\sqrt{3}.\dfrac{1}{\sqrt{3}}\)
\(=-5\)
\(K=\sqrt{125}-4\sqrt{45}+3\sqrt{20}-\sqrt{80}\)
\(=\sqrt{5^2.5}-4\sqrt{3^2.5}+3\sqrt{2^2.5}-\sqrt{4^2.5}\)
\(=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5}\)
\(=\sqrt{5}.\left(5-12+6-4\right)\)
\(=-5\sqrt{5}\)
\(L=2\sqrt{9}+\sqrt{25}-5\sqrt{4}\)
\(=2\sqrt{3^2}+\sqrt{5^2}-5\sqrt{2^2}\)
\(=2.3+5-5.2\)
\(=1\)
\(N=2\sqrt{32}-5\sqrt{27}-4\sqrt{8}+3\sqrt{75}\)
\(=2.4\sqrt{2}-5.3\sqrt{3}-4.2\sqrt{2}+3.5\sqrt{3}\)
\(=8\sqrt{2}-8\sqrt{2}-15\sqrt{3}+15\sqrt{3}\)
\(=0\)
\(O=2\sqrt{3.5^2}-3\sqrt{3.2^2}+\sqrt{3.3^2}\)
\(=2.5\sqrt{3}-3.2\sqrt{3}+3\sqrt{3}\)
\(=10\sqrt{3}-6\sqrt{3}+3\sqrt{3}\)
\(=7\sqrt{3}\)
22 tháng 6 2023
\(L=\dfrac{2\sqrt{3}-15\sqrt{3}+8\sqrt{3}}{\sqrt{3}}=2-15+8=-5\)
\(K=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5}=-5\sqrt{5}\)
L=2*3+5-5*2=5-4=1
N=8căn 2-8căn2-15căn3+15căn 3=0
O=10căn 3-6căn3+3căn3=7căn 3
24 tháng 5 2021
a, \(\sqrt{11-2\sqrt{10}}=\sqrt{\left(\sqrt{10}\right)^2-2\sqrt{10}+1}=\sqrt{\left(\sqrt{10}+1\right)^2}\)
\(=\left|\sqrt{10}+1\right|=\sqrt{10}+1\)
b, \(\sqrt{27-10\sqrt{2}}=\sqrt{5^2-10\sqrt{2}+\left(\sqrt{2}\right)^2}=\sqrt{\left(5-\sqrt{2}\right)^2}\)
\(=\left|5-\sqrt{2}\right|=5-\sqrt{2}\)
c, \(\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}\right)^2+2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left|\sqrt{3}+1\right|=\sqrt{3}+1\)
làm nốt 2 câu cuối nhé, cách làm y trên
25 tháng 5 2021
d/\(\sqrt{9+4\sqrt{5}}\)
= \(\sqrt{2^2+4\sqrt{5}+\left(\sqrt{5}\right)^2}\)
=\(\sqrt{\left(2+\sqrt{5}\right)^2}\)
= \(\left|2+\sqrt{5}\right|\)
= \(2+\sqrt{5}\)
e/ \(\sqrt{21+4\sqrt{5}}\)
= \(\sqrt{20+4\sqrt{5}+1}\)
=\(\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}+1^2}\)
=\(\sqrt{\left(2\sqrt{5}+1\right)^2}\)
= \(\left|2\sqrt{5}+1\right|\)
= \(2\sqrt{5}+1\)
18 tháng 6 2021
`(5sqrt{1/5}+1/2sqrt{20}-5/4sqrt{4/5}+sqrt{5}):2/5
`=(sqrt5+1/2*2sqrt5-sqrt{5/4}+sqrt5):2/5`
`=(sqrt5+sqrt5+sqrt5-sqrt5/2):2/5`
`=(5/2*sqrt5):2/5`
`=25/4sqrt5`
18 tháng 6 2021
`1/3sqrt{48}+3sqrt{75}-sqrt{27}-10sqrt{1 1/3}`
`=1/3*4sqrt3+3*5sqrt3-3sqrt3-10sqrt{4/3}`
`=4/sqrt3+15sqrt3-3sqrt3-20/sqrt3`
`=12sqrt3-16/sqrt3`
24 tháng 5 2021
a,
\(=\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}-1\right)^2}=\left|\sqrt{5}-1\right|=\sqrt{5}-1\)
b, \(\sqrt{8-\sqrt{60}}=\sqrt{8-\sqrt{4.15}}=\sqrt{8-2\sqrt{15}}\)
\(=\sqrt{8-2\sqrt{3}\sqrt{5}}=\sqrt{\left(\sqrt{5}\right)^2-2\sqrt{3}\sqrt{5}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}=\left|\sqrt{5}-\sqrt{3}\right|=\sqrt{5}-\sqrt{3}\)
2 câu cuối tự làm nhé
30 tháng 6 2023
\(=2\sqrt{80\sqrt{3}}+3\sqrt{20\sqrt{3}}-2\sqrt{5\sqrt{3}}-4\sqrt{45\sqrt{3}}\)
\(=8\sqrt{5\sqrt{3}}+6\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-12\sqrt{5\sqrt{3}}\)
=0
21 tháng 6 2023
a: \(A=6\sqrt{3}+10\sqrt{3}-12\sqrt{3}=4\sqrt{3}\)
b: \(B=7\sqrt{3}+5\sqrt{3}-12\sqrt{3}=0\)
c: \(=12\sqrt{2}-6+3\left(9-4\sqrt{2}\right)=12\sqrt{2}-6+27-12\sqrt{2}=21\)
d: \(=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}=4\sqrt{5}\)
PN
3
NV
Nguyễn Việt Lâm
Giáo viên
12 tháng 9 2021
\(\sqrt{8-2\sqrt{7}}=\sqrt{\left(\sqrt{7}-1\right)^2}=\left|\sqrt{7}-1\right|=\sqrt{7}-1\)
\(\sqrt{29-12\sqrt{5}}-\sqrt{9-4\sqrt{5}}=\sqrt{\left(2\sqrt{5}-3\right)^2}-\sqrt{\left(\sqrt{5}-2\right)^2}\)
\(=\left|2\sqrt{5}-3\right|-\left|\sqrt{5}-2\right|=2\sqrt{5}-3-\sqrt{5}+2=\sqrt{5}-1\)
12 tháng 9 2021
b)\(=\sqrt{\left(\sqrt{7}-1\right)^2}=\sqrt{7}-1\)
c)\(=\sqrt{\left(2\sqrt{5}-3\right)^2}-\sqrt{\left(\sqrt{5}-2\right)^2}\)
\(=2\sqrt{5}-3-\sqrt{5}+2\)
\(=\sqrt{5}-1\)
17 tháng 1 2022
a) \(A=2\sqrt{8}-3\sqrt{32}+\sqrt{50}\)
\(A=2\sqrt{4.2}-3\sqrt{16.2}+\sqrt{25.2}\)
\(A=2.2\sqrt{2}-3.4\sqrt{2}+5\sqrt{2}\)
\(A=4\sqrt{2}-12\sqrt{2}+5\sqrt{2}\)
\(A=\left(4-12+5\right)\sqrt{2}\)
\(A=-3\sqrt{2}\)
b) \(B=\sqrt{12}+4\sqrt{27}-3\sqrt{48}\)
\(B=\sqrt{4.3}+4\sqrt{9.3}-3\sqrt{16.3}\)
\(B=2\sqrt{3}+4.3\sqrt{3}-3.4\sqrt{3}\)
\(B=2\sqrt{3}\)
c) \(C=\sqrt{20a}+4\sqrt{45a}-2\sqrt{125a}\left(a\ge0\right)\)
\(C=\sqrt{4.5a}+4\sqrt{9.5a}-2\sqrt{25.5a}\)
\(C=2\sqrt{5a}+4.3\sqrt{5a}-2.5\sqrt{5a}\)
\(C=2\sqrt{5a}+12\sqrt{5a}-10\sqrt{5a}\)
\(C=\left(2+12-10\right)\sqrt{5a}\)
\(C=4\sqrt{5a}\)
24 tháng 1 2022
a) ta có \(2\sqrt{8}=2\sqrt{4.2}=4\sqrt{2},3\sqrt{32}=3\sqrt{16.2}=12\sqrt{2},\sqrt{50}=\sqrt{25.2}=5\sqrt{2}\) \(\Rightarrow A=4\sqrt{2}-12\sqrt{2}+5\sqrt{2}=-3\sqrt{2}\) b) ta có \(\sqrt{12}=\sqrt{4.3}=2\sqrt{3},4\sqrt{27}=4\sqrt{9.3}=12\sqrt{3},3\sqrt{48}=3\sqrt{16.3}=12\sqrt{3}\Rightarrow B=2\sqrt{3}+12\sqrt{3}-12\sqrt{3}=26\sqrt{3}\)c) ta có \(\sqrt{20a}=\sqrt{4.5a}=2\sqrt{5a},4\sqrt{45a}=4\sqrt{9.5a}=12\sqrt{5a},2\sqrt{125a}=2\sqrt{25.5a}=10\sqrt{5a}\Rightarrow C=2\sqrt{5a}+12\sqrt{5a}-10\sqrt{5a}=4\sqrt{5a}\)