\(VT=2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)
\(=2\sqrt{6}-4\sqrt{2}+1+4\sqrt{2}+8-2\sqrt{6}\)
\(=9=VP\)
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Bài 3: Liên hệ giữa phép nhân và phép khai phương
Các câu hỏi tương tự
Chứng minh :
a) \(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{17}}=8\)
b) \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
Bài 1 : Rút gọn
a) \(\frac{\sqrt{6}+\sqrt{16}}{2\sqrt{3}+\sqrt{28}}\)
b) \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3+\sqrt{4}}}\)
Bài 2: Chứng minh
a)\(\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}=8\)
b)\(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
Tính
1) sqrt{18}.sqrt{2}
2) sqrt{15^2-9^2}
3) sqrt{46-6sqrt{5}}-sqrt{46+6sqrt{5}}
4)sqrt{21+6sqrt{6}}-sqrt{21-6sqrt{6}}
5) left(2+sqrt{5}right).sqrt{9-4sqrt{5}}
6)left(3-sqrt{2}right).sqrt{7+4sqrt{3}}
7)left(sqrt{3}+sqrt{5}right).sqrt{7-2sqrt{10}}
8)left(sqrt{6}+sqrt{10}right).sqrt{4-sqrt{15}}
9) sqrt{2}.left(sqrt{8}-sqrt{32}+3sqrt{18}right)
10) sqrt{2}left(sqrt{2}-sqrt{3-sqrt{5}}right)
11) sqrt{3}-sqrt{2}-sqrt{left(sqrt{3}+sqrt{2}right)^2}
12) left(sqrt{2}-sqrt{3+sqrt{5}}right).sqrt...
Đọc tiếp
Tính
1) \(\sqrt{18}.\sqrt{2}\)
2) \(\sqrt{15^2-9^2}\)
3) \(\sqrt{46-6\sqrt{5}}-\sqrt{46+6\sqrt{5}}\)
4)\(\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)
5) \(\left(2+\sqrt{5}\right).\sqrt{9-4\sqrt{5}}\)
6)\(\left(3-\sqrt{2}\right).\sqrt{7+4\sqrt{3}}\)
7)\(\left(\sqrt{3}+\sqrt{5}\right).\sqrt{7-2\sqrt{10}}\)
8)\(\left(\sqrt{6}+\sqrt{10}\right).\sqrt{4-\sqrt{15}}\)
9) \(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
10) \(\sqrt{2}\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
11) \(\sqrt{3}-\sqrt{2}-\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
12) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
A)left(3-2sqrt{2}right).left(3+2sqrt{2}right) B) sqrt{left(sqrt{3}-2right)}^2-sqrt{left(sqrt{3}+2right)}^2 C)sqrt{3-2sqrt[]{2}}-sqrt{3+2sqrt{2}}
D)left(1+sqrt{3}-sqrt{2}right).left(1+sqrt{3}+2right)
E) left(sqrt{3-sqrt{5}}+sqrt{3+sqrt{5}}right)^2 F)sqrt{15-sqrt{216}}+sqrt{33-12sqrt{6}}
H)sqrt{8sqrt{3}}-2sqrt{25sqrt{12}}+4sqrt{sqrt{192}}
Đọc tiếp
A)\(\left(3-2\sqrt{2}\right).\left(3+2\sqrt{2}\right)\) B) \(\sqrt{\left(\sqrt{3}-2\right)}^2-\sqrt{\left(\sqrt{3}+2\right)}^2\) C)\(\sqrt{3-2\sqrt[]{2}}-\sqrt{3+2\sqrt{2}}\)
D)\(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+2\right)\)
E) \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\) F)\(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
H)\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
Bài 1 : Rút gọn biểu thức sau :
frac{sqrt{2}+sqrt{3}+sqrt{6}+sqrt{8}+sqrt{16}}{sqrt{2}+sqrt{3}+sqrt{4}}
Bài 2 : Chứng minh đẳng thức sau :
sqrt{8+2sqrt{10+2sqrt{5}}}.sqrt{8-2sqrt{10+2sqrt{5}}}2sqrt{5}-2
Bài 3 : Cho biểu thức E left(frac{sqrt{x}+1}{sqrt{x}-1}-frac{sqrt{x}-1}{sqrt{x}+1}+4sqrt{x}right):left(sqrt{x}-frac{1}{sqrt{x}}right)
a) Rút gọn biẻu thức E
b) Tính giá trị của E khi x left(4+sqrt{15}right)left(sqrt{10}-sqrt{6}right)sqrt{4-sqrt{15}}
Đọc tiếp
Bài 1 : Rút gọn biểu thức sau :
\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
Bài 2 : Chứng minh đẳng thức sau :
\(\sqrt{8+2\sqrt{10+2\sqrt{5}}}.\sqrt{8-2\sqrt{10+2\sqrt{5}}}=2\sqrt{5}-2\)
Bài 3 : Cho biểu thức E = \(\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}+4\sqrt{x}\right):\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)\)
a) Rút gọn biẻu thức E
b) Tính giá trị của E khi x = \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
Thực hiện phép tính:
a) ( 4+sqrt{15})left(sqrt{10}-sqrt{6}right)sqrt{4-sqrt{15}}
b)sqrt{3-sqrt{5}}left(3+sqrt{5}right)left(sqrt{10}-sqrt{2}right)
c) left(sqrt{3}-sqrt{2}+1right)left(sqrt{3}-1right)
d) sqrt{2+sqrt{3}}.sqrt{2+sqrt{2+sqrt{3}}}.sqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}.sqrt{2-sqrt{2+sqrt{2+sqrt{3}}}}
Đọc tiếp
Thực hiện phép tính:
a) ( \(4+\sqrt{15}\))\(\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\)
c) \(\left(\sqrt{3}-\sqrt{2}+1\right)\left(\sqrt{3}-1\right)\)
d) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
29 tháng 7 2020 lúc 8:35
Rút gọn
\(\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{18}}\)
\(\left(\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\right).\left(15+2\sqrt{6}\right)\)
Tính :
a) \(\sqrt{3\sqrt{2}+2\sqrt{3}}.\sqrt{3\sqrt{2}-2\sqrt{3}}\)
b) \(\left(1-\sqrt{2}+\sqrt{3}\right)\left(1+\sqrt{2}-\sqrt{3}\right)\)
c) \(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\)
Rút gọn biểu thức
a. left(2sqrt{5}-sqrt{7}right)left(2sqrt{5}+sqrt{7}right)
b.left(5sqrt{2}+2sqrt{3}right)left(2sqrt{3}-5sqrt{2}right)
c. sqrt{9+4sqrt{5}}
d. sqrt{14-6sqrt{5}}+sqrt{14+6sqrt{5}}
e. sqrt{55-6sqrt{6}}
f. sqrt{21-6sqrt{6}}
Đọc tiếp
Rút gọn biểu thức
a. \(\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}+\sqrt{7}\right)\)
b.\(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)
c. \(\sqrt{9+4\sqrt{5}}\)
d. \(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)
e. \(\sqrt{55-6\sqrt{6}}\)
f. \(\sqrt{21-6\sqrt{6}}\)