căn baacjhai của 21,8^2-18,2^2
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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) \(\sqrt{21,8^2-18,2^2}\)
\(=\sqrt{\left(21,8-18,2\right).\left(21,8+18,2\right)}\)
\(=\sqrt{3,6.40}=\sqrt{4.36}=2.6=12\)
\(a,\sqrt{68^2-32^2}\)
\(=\sqrt{\left(68-32\right)\left(68+32\right)}\)
\(=\sqrt{3600}=60\)
\(b,\sqrt{37^2-12^2}\)
\(=\sqrt{\left(37-12\right)\left(37+12\right)}\)
\(=\sqrt{25.49}=5.7=35\)
\(c,\sqrt{21,8^2-18,2^2}\)
\(=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}\)
\(=\sqrt{40.3,6}=12\)
\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\frac{\sqrt{0,5}.\sqrt{25}}{\sqrt{0,5}}=\sqrt{25}=5\)
\(\frac{\sqrt{6}}{\sqrt{150}}=\frac{\sqrt{6}}{\sqrt{6}.\sqrt{25}}=\frac{1}{\sqrt{25}}=\frac{1}{5}\)
\(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8+3,2\right)\left(6,8-3,2\right)}=\sqrt{10.3,6}=\sqrt{36}=6\)
\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}=\sqrt{40.3,6}=\sqrt{144}=12\)
\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\frac{12,5}{0,5}}=\sqrt{25}=5\)
\(\frac{\sqrt{6}}{\sqrt{150}}=\sqrt{\frac{6}{150}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\)
\(\sqrt{\left(6,8\right)^2-\left(3,2\right)^2}=\sqrt{46,24-10,24}=\sqrt{36}=6\)
\(\sqrt{\left(21,8\right)^2-\left(18,2\right)^2}=\sqrt{475,24-331,24}=\sqrt{144}=12\)
\(a=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}=\sqrt{3,6\left(10\right)}=\sqrt{36}=6\)
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)\(\sqrt{146,5^2-109,5^2+27.256}\)=\(\sqrt{\left(146,5-109,5\right)\left(146,5+109,5\right)+27.256}\)
=\(\sqrt{37.256+\sqrt{27.256}}=\sqrt{64.256}=\sqrt{64}.\sqrt{256}=128\)
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,
\(A=7+4\sqrt{3}+\sqrt{3}-1\\ =6+5\sqrt{3}\\ B=7+2\sqrt{10}-\left(11+2\sqrt{10}\right)\\ =7+2\sqrt{10}-11-2\sqrt{10}\\ =-4\)
\(31,8^2-2.31,8.21,8+21,8^2\)
\(=\left(31,8-21,8\right)^2=10^2=100\)
\(58,2^2+2.58,2.41,8+41,8^2\)
\(=\left(58,2+41,8\right)^2=100^2=10000\)
Cái đó áp dụng HDT binh phương của 1 hiệu =>(31,8-21,8)2=102=100