1,Rút gọn:
\((3\sqrt{2}+\sqrt{10})(\sqrt{28}-12\sqrt{5})\)
1,Rút gọn:
\((3\sqrt{2}+\sqrt{10})(\sqrt{28}-12\sqrt{5)}\)
Rút gọn:
\((3\sqrt{2}+\sqrt{10})(\sqrt{28}-12\sqrt{5})\)
1,Rút gọn:
\((3\sqrt{2}+\sqrt{10})(\sqrt{28}-12\sqrt{5})\)
Giúp mình với!!!
Rút gọn: (Giải chi tiết từng bước)
9) \(2\sqrt{8\sqrt{3}-2\sqrt{5\sqrt{3}}}-3\sqrt{20\sqrt{3}}\)
10) \(\sqrt{12x}-\sqrt{48x}-3\sqrt{3x}+27\) với x \(\ge\) 0
11) \(\sqrt{18x}-5\sqrt{8x}+7\sqrt{18x}+28\) với \(x\ge0\)
12) \(\sqrt{45a}-\sqrt{20a}+4\sqrt{45a}+\sqrt{a}\) với \(a\ge0\)
Cần gấp ạ
9) Sửa: \(2\sqrt{8\sqrt{3}}-2\sqrt{5\text{ }\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
\(=2\sqrt{2^2\cdot2\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{2^2\cdot5\sqrt{3}}\)
\(=2\cdot2\sqrt{2\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\cdot2\sqrt{5\sqrt{3}}\)
\(=4\sqrt{2\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}\)
\(=4\sqrt{2\sqrt{3}}-8\sqrt{5\sqrt{3}}\)
10) \(\sqrt{12x}-\sqrt{48x}-3\sqrt{3x}+27\)
\(=\sqrt{2^2\cdot3x}-\sqrt{4^2\cdot3x}-3\sqrt{3x}+27\)
\(=2\sqrt{3x}-4\sqrt{3x}-3\sqrt{3x}+27\)
\(=-5\sqrt{3x}++27\)
11) \(\sqrt{18x}-5\sqrt{8x}+7\sqrt{18x}+28\)
\(=\sqrt{3^2\cdot2x}-5\sqrt{2^2\cdot2x}+7\sqrt{3^2\cdot2x}+28\)
\(=3\sqrt{2x}-5\cdot2\sqrt{2x}+7\cdot3\sqrt{2x}+28\)
\(=3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}+28\)
\(=14\sqrt{2x}+28\)
12) \(\sqrt{45a}-\sqrt{20a}+4\sqrt{45a}+\sqrt{a}\)
\(=\sqrt{3^2\cdot5a}-\sqrt{2^2\cdot5a}+4\sqrt{3^2\cdot5a}+\sqrt{a}\)
\(=3\sqrt{5a}-2\sqrt{5a}+4\cdot3\sqrt{5a}+\sqrt{a}\)
\(=3\sqrt{5a}-2\sqrt{5a}+12\sqrt{5a}+\sqrt{a}\)
\(=13\sqrt{5a}+\sqrt{a}\)
Rút gọn biểu thức: \(P=\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}-\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3}-\sqrt{5}}+\frac{\left(\sqrt{5}-1\right).\sqrt[3]{2+\sqrt{5}}}{\sqrt{28}-10\sqrt{3}+\sqrt{3}}\)
Giúp mk nha!
Xem kỹ lại đề nhé! loại này đề lệch một tý thôi -->Không rút được !
p/s: Tránh truongf hợp làm đến cuối mới biết đề sai.
Rút gọn các biểu thức sau:
a) \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}-\sqrt{20}\)
b) \(\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\dfrac{10}{1+\sqrt{6}}\)
a: Ta có: \(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}-\sqrt{20}\)
\(=4\sqrt{7}+6\sqrt{7}-15\sqrt{7}+4\sqrt{7}-2\sqrt{5}\)
\(=-\sqrt{7}-2\sqrt{5}\)
Rút gọn biểu thức
a) \(2\sqrt{28}+\sqrt{63}-\sqrt{112}\)
b) \(3\sqrt{48}-5\sqrt{108}+6\sqrt{\dfrac{1}{3}}\)
`a)2\sqrt{28}+\sqrt{63}-\sqrt{112}`
`=4\sqrt{7}+3\sqrt{7}-4\sqrt{7}`
`=3\sqrt{7}`.
`b)3\sqrt{48}-5\sqrt{108}+6\sqrt{1/3}`
`=12\sqrt{3}-30\sqrt{3}+2\sqrt{[3^2]/3}`
`=-18\sqrt{3}+2\sqrt{3}`
`=-16\sqrt{3}`.
5.Rút gọn:
B= \(\sqrt{6-2\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-8\sqrt{2}}}}\)
6.Rút gọn:
A= \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
Rút gọn biểu thức
1) \(\sqrt{9+4\sqrt{5}}\) - \(\sqrt{9-4\sqrt{5}}\)
2) \(\sqrt{12-6\sqrt{3}}\) + \(\sqrt{12+6\sqrt{3}}\)
1) \(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
\(=\sqrt{2^2+2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}-\sqrt{2^2-2\cdot2\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}\)
\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)
\(=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|\)
\(=2+\sqrt{5}+2-\sqrt{5}\)
\(=4\)
2) \(\sqrt{12-6\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)
\(=\sqrt{3^2-2\cdot3\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{3^2+2\cdot3\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(3-\sqrt{3}\right)^2}+\sqrt{\left(3+\sqrt{3}\right)^2}\)
\(=\left|3-\sqrt{3}\right|+\left|3+\sqrt{3}\right|\)
\(=3-\sqrt{3}+3+\sqrt{3}\)
\(=6\)