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a) \(\sqrt{117,5^2-26,5^2-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\)
\(=\sqrt{91.144-1440}=\sqrt{144\left(91-10\right)}=\sqrt{12^2.9^2}=12.9=108\)
b) \(\sqrt{146,5^2-109,5^2+27.256}=\sqrt{\left(146,5-109,5\right)\left(146,5+109,5\right)+27.256}\)
\(=\sqrt{37.256+27.256}=\sqrt{256\left(37+27\right)}=\sqrt{256.64}=\sqrt{16^2.8^2}=16.8=128\)
a) \(\sqrt{117.5^2-26.5^2-1440}\)
\(=\sqrt{5^2\left(117-26\right)-1440}\)
\(=5\sqrt{177-26-1440}\)
\(=5\sqrt{-1289}\)
\(=-5\sqrt{1289}\)
Câu B tương tự .
E ms lên lớp 9 sai thì thôi nha
\(\sqrt{117,5^2-26,5^2}-1440=-202475\)
\(\sqrt{146,5^2-109,5^2+27,256=}-11816494\)
A=(\(\sqrt{13}\).\(\sqrt{2}\)+5\(\sqrt{2}\))\(\sqrt{19-5\sqrt{13}}\)
=(\(\sqrt{13}\)+5)\(\sqrt{2}\). \(\sqrt{19-5\sqrt{13}}\)
=(\(\sqrt{13}\)+5) \(\sqrt{2\left(19-5\sqrt{13}\right)}\)
= (\(\sqrt{13}\)+5) \(\sqrt{38-2.5\sqrt{13}}\)
=(\(\sqrt{13}\)+5) \(\sqrt{5^2-2.5\sqrt{13}+13}\)
=(\(\sqrt{13}\)+5)\(\sqrt{\left(5-\sqrt{13}\right)^2}\)
=(\(\sqrt{13}\)+5) \(|5-\sqrt{13}|\)
=(5+\(\sqrt{13}\))(5-\(\sqrt{13}\))
= 25-13 = 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)\(\sqrt{146,5^2-109,5^2+27.256}\)=\(\sqrt{\left(146,5-109,5\right)\left(146,5+109,5\right)+27.256}\)
=\(\sqrt{37.256+\sqrt{27.256}}=\sqrt{64.256}=\sqrt{64}.\sqrt{256}=128\)
\(2\sqrt{\left(-5\right)^6}+3\sqrt{\left(-2\right)^8}.\)
\(=2\sqrt{\left(\left(-5\right)^3\right)^2}+3\sqrt{\left(\left(-2\right)^4\right)^2}\)
\(=2\cdot\left(-5\right)^3+3\cdot\left(-2\right)^4\)
\(=2\cdot125+3\cdot16=250+48=298\)
\(\Rightarrow2\sqrt{\left(-5\right)^6}+3\sqrt{\left(-2\right)^8}=298\)
\(2\sqrt{\left(-5\right)^6}+3\sqrt{\left(-2\right)^8}\)
\(=2\times125+3\times16\)
\(=250+48\)
\(=298\)
