Bài 3: Thực hiện các phép tính sau:
a) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
b) \(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
c) \(\sqrt{6-4\sqrt{2}}+\)\(\sqrt{22-12\sqrt{2}}\)
hộ mk với
Thực hiện các phép tính sau:
a) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
b) \(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
c) \(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
a,\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}=\sqrt{2^2+2\cdot2\cdot\left(2\sqrt{5}\right)+\left(2\sqrt{5}\right)^2}\) \(+\sqrt{\left(\sqrt{5}\right)^2-2\cdot2\sqrt{5}+2^2}=\sqrt{\left(2+2\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)=\(2+2\sqrt{5}+\sqrt{5}-2=3\sqrt{5}\)
b,\(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}=3-2\sqrt{2}+2\sqrt{2}+1=4\)
c,\(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}=2-\sqrt{2}+3\sqrt{2}-2=2\sqrt{2}\)
câu b với câu c giải thích ra dùm e đc kh ạ?
Thực hiện phép tính:
a)\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
b)\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
c)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
d)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
a,\(\sqrt{\left(\sqrt{3}-1\right)^2}\) \(+\sqrt{\left(\sqrt{3}+1\right)^2}=2\sqrt{3}\)
b. \(\sqrt{\left(2\sqrt{5}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}=3\sqrt{5}\)
c,\(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{\left(2\sqrt{2}+1\right)^2}=4\)
d.\(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(3\sqrt{2}-2\right)^2}=2\sqrt{2}\)
thực hiện phép tính
a)\(\sqrt{6+2\sqrt{5}}-\sqrt{62\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
c) \(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{ }5}\)
e)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g) \(\sqrt{43+24\sqrt{3}}-\sqrt{49-8\sqrt{3}}\)
cho cách làm dạng bài này luôn. Chỗ nào chưa hiểu thì nói tớ sẽ giải thích thêm (cần góp ý để hoàn thiện thêm phần hướng dẫn đó mà. Cảm ơn cậu).
Phương Nam Phim (à quên, Từ Hạ) hân hạnh giới thiệu bộ phim...
Thực hiện phép tính (rút gọn biểu thức)
a) \(\sqrt{9+4\sqrt{5}}\) - \(\sqrt{9-4\sqrt{5}}\)
b) \(\sqrt{12-6\sqrt{3}}\) + \(\sqrt{12+6\sqrt{3}}\)
c) \(\sqrt{6\sqrt{2}+11}\) - \(\sqrt{11-6\sqrt{2}}\)
Lời giải:
a.
\(=\sqrt{5+2.2\sqrt{5}+2^2}-\sqrt{5-2.2\sqrt{5}+2^2}\)
$=\sqrt{(\sqrt{5}+2)^2}-\sqrt{(\sqrt{5}-2)^2}$
$=|\sqrt{5}+2|-|\sqrt{5}-2|=(\sqrt{5}+2)-(\sqrt{5}-2)=4$
b.
$=\sqrt{3-2.3\sqrt{3}+3^2}+\sqrt{3+2.3.\sqrt{3}+3^2}$
$=\sqrt{(\sqrt{3}-3)^2}+\sqrt{(\sqrt{3}+3)^2}$
$=|\sqrt{3}-3|+|\sqrt{3}+3|$
$=(3-\sqrt{3})+(\sqrt{3}+3)=6$
c.
$=\sqrt{2+2.3\sqrt{2}+3^2}-\sqrt{2-2.3\sqrt{2}+3^2}$
$=\sqrt{(\sqrt{2}+3)^2}-\sqrt{(\sqrt{2}-3)^2}$
$=|\sqrt{2}+3|-|\sqrt{2}-3|$
$=(\sqrt{2}+3)-(3-\sqrt{2})=2\sqrt{2}$
Thực hiện phép tính:
a)\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
b)\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
c)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
d)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
a,
\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\\ =\sqrt{3-2\sqrt{3}+1}+\sqrt{3+2\sqrt{3}+1}\\ =\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\\ =\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|\\ =\sqrt{3}-1+\sqrt{3}+1\\ =2\sqrt{3}\)
b,
\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\\ =\sqrt{24+4\cdot\sqrt{4}\cdot\sqrt{5}}+\sqrt{9-4\sqrt{5}}\\ =\sqrt{24+4\sqrt{20}}+\sqrt{9-4\sqrt{5}}\\ =\sqrt{20+4\sqrt{20}+4}+\sqrt{5-4\sqrt{5}+4}\\ =\sqrt{\left(\sqrt{20}+4\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\\ =\left|\sqrt{20}+4\right|+\left|\sqrt{5}-2\right|\\ =\sqrt{20}+4+\sqrt{5}-2\\ =2+2\sqrt{5}+\sqrt{5}\\ =2+3\sqrt{5}\)
c,
\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\\ =\sqrt{17-6\cdot\sqrt{4}\cdot\sqrt{2}}+\sqrt{9+2\cdot\sqrt{4}\cdot\sqrt{2}}\\ =\sqrt{17-6\sqrt{8}}+\sqrt{9+2\sqrt{8}}\\ =\sqrt{9-6\sqrt{8}+8}+\sqrt{8+2\sqrt{8}+1}\\ =\sqrt{\left(3-\sqrt{8}\right)^2}+\sqrt{\left(\sqrt{8}+1\right)^2}\\ =\left|3-\sqrt{8}\right|+\left|\sqrt{8}+1\right|\\ =3-\sqrt{8}+\sqrt{8}+1\\ =4\)
d,
\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\\ =\sqrt{6-4\sqrt{2}}+\sqrt{22-4\cdot\sqrt{9}\cdot\sqrt{2}}\\ =\sqrt{6-4\sqrt{2}}+\sqrt{22-4\sqrt{18}}\\ =\sqrt{4-4\sqrt{2}+2}+\sqrt{18-4\sqrt{18}+4}\\ =\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{18}-2\right)^2}\\ =\left|2-\sqrt{2}\right|+\left|\sqrt{18}-2\right|\\ =2-\sqrt{2}+\sqrt{18}-2\\ =-\sqrt{2}+\sqrt{18}\\ =-\sqrt{2}+3\sqrt{2}\\ =2\sqrt{2}\)
b,
\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\\ =\sqrt{24+4\cdot\sqrt{4}\cdot\sqrt{5}}+\sqrt{9-4\sqrt{5}}\\ =\sqrt{24+4\sqrt{20}}+\sqrt{9-4\sqrt{5}}\\ =\sqrt{20+4\sqrt{20}+4}+\sqrt{5-4\sqrt{5}+4}\\ =\sqrt{\left(\sqrt{20}+2\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\\ =\left|\sqrt{20}+2\right|+\left|\sqrt{5}-2\right|\\ =\sqrt{20}+2+\sqrt{5}-2\\ =\sqrt{20}+\sqrt{5}\\ =\sqrt{4}\cdot\sqrt{5}+\sqrt{5}\\ =2\sqrt{5}+\sqrt{5}\\ =3\sqrt{5} \)
Bài 1. (2,0 điểm) Thực hiện phép tính: n) 7/9 * sqrt(81) - 1/2 * sqrt(16) . c) (sqrt(8/3) - sqrt(24) + sqrt(50/3)) , sqrt 12 . » sqrt((sqrt(7) - 4) ^ 2) + sqrt(7) 1/(5 + 2sqrt(3)) + 1/(5 - 2sqrt(3))
Thực hiện phép tính:
a) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)
c)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{5}}\)
e)\(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
g)\(\sqrt{43+24\sqrt{3}}-\sqrt{49-\sqrt{8\sqrt{3}}}\)
h)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)
Thực hiện các phép tính sau:
a,\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
b,\(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)
c,\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
d,\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)
e,\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
f,\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)
Giải giúp mình với m.n mình đang cần gấp lắm!!!!!
a) \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
\(=\left|\sqrt{3}+\sqrt{2}\right|-\left|\sqrt{3}-\sqrt{2}\right|=\left(\sqrt{3}+\sqrt{2}\right)-\left(\sqrt{3}-\sqrt{2}\right)\)
\(=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}=2\sqrt{2}\)
b) \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)
\(=\left|\sqrt{5}-\sqrt{2}\right|-\left|\sqrt{5}+\sqrt{2}\right|=\left(\sqrt{5}-\sqrt{2}\right)-\left(\sqrt{5}+\sqrt{2}\right)\)
\(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)
c) \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|=\left(\sqrt{3}-1\right)+\left(\sqrt{3}+1\right)\)
\(=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)
d) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}=2\sqrt{6+2\sqrt{5}}+\sqrt{\left(\sqrt{5}-2\right)^2}\)
\(=2\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{5}-2=2\sqrt{5}+2+\sqrt{5}-2=3\sqrt{5}\)
e,
\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\\ =\sqrt{17-6\cdot\sqrt{4}\cdot\sqrt{2}}+\sqrt{9+2\cdot\sqrt{4}\cdot\sqrt{2}}\\ =\sqrt{17-6\cdot\sqrt{8}}+\sqrt{9+2\cdot\sqrt{8}}\\ =\sqrt{9-2\cdot3\cdot\sqrt{8}+8}+\sqrt{8+2\cdot\sqrt{8}\cdot1+1}\\ =\sqrt{3^2-2\cdot3\cdot\sqrt{8}+\sqrt{8}^2}+\sqrt{\sqrt{8}^2+2\cdot\sqrt{8}\cdot1+1^2}\\ =\sqrt{\left(3-\sqrt{8}\right)^2}+\sqrt{\left(\sqrt{8}+1\right)^2}\\ =\left|3-\sqrt{8}\right|+\left|\sqrt{8}+1\right|\\ =3-\sqrt{8}+\sqrt{8}+1\\ =4\)
f,
\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\\ =\sqrt{6-4\sqrt{2}}+\sqrt{22-4\cdot\sqrt{9}\cdot\sqrt{2}}\\ =\sqrt{6-4\sqrt{2}}+\sqrt{22-4\cdot\sqrt{18}}\\ =\sqrt{4-2\cdot2\cdot\sqrt{2}+2}+\sqrt{18-2\cdot2\cdot\sqrt{18}+4}\\ =\sqrt{2^2-2\cdot2\cdot\sqrt{2}+\sqrt{2}^2}+\sqrt{\sqrt{18}^2-2\cdot2\cdot\sqrt{18}+2^2}\\ =\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{18}-2\right)^2}\\ =\left|2-\sqrt{2}\right|+\left|\sqrt{18}-2\right|\\ =2-\sqrt{2}+\sqrt{18}-2\\ =\sqrt{2}+\sqrt{18}\\ =\sqrt{2}+\sqrt{9}\cdot\sqrt{2}\\ =\sqrt{2}+3\sqrt{2}\\ =4\sqrt{2}\)
1. rút gọn biểu thức sau
\(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
2. thực hiện các phép tính sau
a. \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
b. \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
c.\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
1. \(=\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}+\sqrt{3+\sqrt{\left(2\sqrt{3}+1\right)^2}}=\sqrt{5-2\sqrt{3}-1}+\sqrt{3+2\sqrt{3}+1}=\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)
1/ \(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)
\(=\sqrt{5-\left(1+\sqrt{12}\right)^2}+\sqrt{3+\left(1+\sqrt{12}\right)^2}\)
\(=\sqrt{5-\left|1+\sqrt{12}\right|}+\sqrt{3+\left|1+\sqrt{12}\right|}\)
\(=\sqrt{5-1-\sqrt{12}}+\sqrt{3+1+\sqrt{12}}\)
\(=\sqrt{4-\sqrt{12}}+\sqrt{4+\sqrt{12}}\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|\)
\(=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)
2/ a) \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)
b) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
\(=\sqrt{\left(1+\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=\left|1+\sqrt{5}\right|-\left|\sqrt{5}-1\right|=1+\sqrt{5}-\sqrt{5}+1=2\)
c) \(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)
\(=\sqrt{\left(\sqrt{9}-\sqrt{8}\right)^2}+\sqrt{\left(1+\sqrt{8}\right)^2}\)
\(=\left|\sqrt{9}-\sqrt{8}\right|+\left|1+\sqrt{8}\right|\)
\(=\sqrt{9}-\sqrt{8}+1+\sqrt{8}=3+1=4\)
Chúc các bạn học tốt nhá!