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\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\frac{\sqrt{0,5}.\sqrt{25}}{\sqrt{0,5}}=\sqrt{25}=5\)
\(\frac{\sqrt{6}}{\sqrt{150}}=\frac{\sqrt{6}}{\sqrt{6}.\sqrt{25}}=\frac{1}{\sqrt{25}}=\frac{1}{5}\)
\(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8+3,2\right)\left(6,8-3,2\right)}=\sqrt{10.3,6}=\sqrt{36}=6\)
\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}=\sqrt{40.3,6}=\sqrt{144}=12\)
\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\frac{12,5}{0,5}}=\sqrt{25}=5\)
\(\frac{\sqrt{6}}{\sqrt{150}}=\sqrt{\frac{6}{150}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\)
\(\sqrt{\left(6,8\right)^2-\left(3,2\right)^2}=\sqrt{46,24-10,24}=\sqrt{36}=6\)
\(\sqrt{\left(21,8\right)^2-\left(18,2\right)^2}=\sqrt{475,24-331,24}=\sqrt{144}=12\)
\(a=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}=\sqrt{3,6\left(10\right)}=\sqrt{36}=6\)
a) \(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}\)
=\(\sqrt{3,6.10}=\sqrt{36}=6\)
b)\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}\)
=\(\sqrt{3,6.40}=\sqrt{144}=12\)
c)\(\sqrt{117,5^2-26,5^2-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\)
=\(\sqrt{91.144-1440}=\sqrt{144.81}=\sqrt{144}.\sqrt{81}=108\)
d)\(\sqrt{146,5^2-109,5^2+27.256}\)=\(\sqrt{\left(146,5-109,5\right)\left(146,5+109,5\right)+27.256}\)
=\(\sqrt{37.256+\sqrt{27.256}}=\sqrt{64.256}=\sqrt{64}.\sqrt{256}=128\)
\(a,\sqrt{68^2-32^2}\)
\(=\sqrt{\left(68-32\right)\left(68+32\right)}\)
\(=\sqrt{3600}=60\)
\(b,\sqrt{37^2-12^2}\)
\(=\sqrt{\left(37-12\right)\left(37+12\right)}\)
\(=\sqrt{25.49}=5.7=35\)
\(c,\sqrt{21,8^2-18,2^2}\)
\(=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}\)
\(=\sqrt{40.3,6}=12\)
1,
\(a,=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}\\ =\sqrt{3,6\cdot40}\\ =\sqrt{36\cdot4}\\ =\sqrt{36}\cdot\sqrt{4}\\ =6\cdot4\\ =24\)
\(b,=10\cdot\sqrt{\left(6,5-1,6\right)\left(6,5+1,6\right)}\\ =10\cdot\sqrt{4,9\cdot8,1}\\ =10\cdot\sqrt{49\cdot0,81}\\ =10\cdot\sqrt{49}\cdot\sqrt{0,81}\\ =10\cdot7\cdot0,9\\ =63\)
2,
\(A=7+4\sqrt{3}+\sqrt{3}-1\\ =6+5\sqrt{3}\\ B=7+2\sqrt{10}-\left(11+2\sqrt{10}\right)\\ =7+2\sqrt{10}-11-2\sqrt{10}\\ =-4\)
Lời giải:
$\sqrt{6,8^2-3,2^2}=\sqrt{(6,8-3,2)(6,8+3,2)}=\sqrt{3,6.10}=\sqrt{36}=6$
Akai Haruma Em xin lỗi nhưng có thể giúp e bài này đc k ạ
Câu hỏi của Hàn Thất - Toán lớp 8 | Học trực tuyến
\(B=\left(\sqrt{10}+\sqrt{6}\right).\sqrt{8-2\sqrt{15}}\)
\(=\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
\(=\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left|\sqrt{5}-\sqrt{3}\right|\)
\(=\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)\) (vì\(\sqrt{5}-\sqrt{3}>0\))
\(=2\sqrt{2}\)
\(A=\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right).\sqrt{2}\)
\(=\sqrt{4}-\sqrt{6-2\sqrt{5}}\)
\(=\sqrt{4}-\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(=\sqrt{4}-\left|\sqrt{5}-1\right|\)
\(=\sqrt{4}-\sqrt{5}+1\) (vì \(\sqrt{5}-1>0\))
a) Ta có: \(A=2\sqrt{2+\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
\(\Leftrightarrow A=2\sqrt{2+\sqrt{5-\sqrt{12+1+2\sqrt{12}}}}\)
\(\Leftrightarrow A=2\sqrt{2+\sqrt{5-\sqrt{\left(\sqrt{12}+1\right)^2}}}\)
\(\Leftrightarrow A=2\sqrt{2+\sqrt{5-\sqrt{12}+1}}\)
\(\Leftrightarrow A=2\sqrt{2+\sqrt{3+1-2\sqrt{3}}}\)
\(\Leftrightarrow A=2\sqrt{2+\sqrt{\left(\sqrt{3}-1\right)^2}}\)
\(\Leftrightarrow A=2\sqrt{2+\sqrt{3}-1}\)
\(\Leftrightarrow A=2\sqrt{\sqrt{3}+1}\)
\(\Leftrightarrow A\approx3,30578\)
b) Ta có: \(B=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(\Leftrightarrow B=\sqrt{4+2\sqrt{2}}.\sqrt{4-\left(2+\sqrt{2}\right)}\)
\(\Leftrightarrow B=\sqrt{2}.\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}\)
\(\Leftrightarrow B=\sqrt{2}.\left(4-2\right)\)
\(\Leftrightarrow B=2\sqrt{2}\)
\(\Leftrightarrow B\approx2,82843\)
Câu 1:
a, \(\sqrt{50.98} = 5\sqrt{2} . 7\sqrt{2} = 70\)
b, \(\sqrt{2,5.12,1} = 30,25\)
c, \(\sqrt{17.51.27} = \sqrt{23409} = 153\)
d, \(\sqrt{32.128} = \sqrt{4096} = 64\)
e, \(\sqrt{3,2.7,2.49} = 7\sqrt{3,2.7,2} = 7\sqrt{23,04} =33,6\)
g, \(\sqrt{2,5.12,5.20} = \sqrt{625} = 25\)
a) \(\sqrt{6,8^2-3.2^2}\)
\(=\sqrt{\left(6,8+3,2\right).\left(6,8-3,2\right)}\)
\(=\sqrt{3,6.10}=\sqrt{36}=6\)
b) \(\sqrt{21,8^2-18,2^2}\)
\(=\sqrt{\left(21,8-18,2\right).\left(21,8+18,2\right)}\)
\(=\sqrt{3,6.40}=\sqrt{4.36}=2.6=12\)