Rút gọn rồi tính:
a)\(\sqrt{117,5^2-26,5^2-1440}\)
b)\(\sqrt{146,5^2-109,5^2+27.256}\)
Rút gọn rồi tính:
a.\(\sqrt{117,5^2-26,5^2-1440}\)
b, \(\sqrt{146,5^2-109,5^2+27.256}\)
Mong mọi người giúp đỡ
\(\sqrt{117,5^2-26,5^2}-1440=-202475\)
\(\sqrt{146,5^2-109,5^2+27,256=}-11816494\)
câu đc của bạn phương thiếu căn ở 1440
câu a đc 108
câu b đc128
Rút gọn rồi tính :
a) \(\sqrt{6,8^2-3,2^2}\)
b) \(\sqrt{21,8^2-18,2^2}\)
c) \(\sqrt{117,5^2-26,5^2-1440}\)
d) \(\sqrt{146,5^2-109,5^2+27.256}\)
\(a=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}=\sqrt{3,6\left(10\right)}=\sqrt{36}=6\)
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.Rút gọn rồi tính:
a) \(\sqrt{117,5^2-26,5^2-1440}\)
b) \(\sqrt{146,5^2-109,5^2+27\times256}\)
2. So sánh:
\(\sqrt{2003}+\sqrt{2005}\)và \(2\sqrt{2004}\)
2)
\(\left(\sqrt{2003}+\sqrt{2005}\right)^2=2003+2005+2\sqrt{2003\times2005}\)\(=4008+2\sqrt{\left(2004-1\right)\left(2004+1\right)}=4008+2\sqrt{2004^2-1}\)
\(\left(\sqrt{2004}+\sqrt{2004}\right)^2=2004+2004+2\sqrt{2004\times2004}\)\(=4008+2\sqrt{2004^2}\)
Ta có \(2004^2>2004^2-1\Rightarrow\sqrt{2004^2}>\sqrt{2004^2-1}\Rightarrow4008+2\sqrt{2004^2}>4008+2\sqrt{2004^2-1}\)
Vậy \(2\sqrt{2004}>\sqrt{2003}+\sqrt{2005}\)
Bài 1:Rút gọn
a,\(\sqrt{117,5^2-26,5^2-1440}\)
b,\(\sqrt{146,5^2-109,5^2+27,256}\)
c,\(\sqrt{9-\sqrt{17}\cdot\sqrt{9+\sqrt{17}}}\)
Rút gọn rồi tính @@
\(\sqrt{146,5^2-109,5^2+27,256}\)
Thực hiện phép tính
\(\sqrt{146,5^2-109,5^2+27.256}\)
\(\sqrt{117,5^2-26,5^2-1440}\)
\(=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\\ =\sqrt{91\cdot144-1440}=\sqrt{144\left(91-10\right)}\\ =\sqrt{144\cdot81}=\sqrt{144}\cdot\sqrt{81}=12\cdot9=108\)
c, \(\sqrt{117,5^2-26,5^2-1440}\)
c) \(\sqrt{117,5^2-26,5^2-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-144.10}\)
\(=\sqrt{144.91-144.10}=\sqrt{144.\left(91-10\right)}=12\sqrt{81}=12.9=108\)
\(\sqrt{117.5^2-26.5^2-1440}\)
\(=\sqrt{\left(117.5-26.5\right)\left(117.5+26.5\right)-1440}\)
\(=\sqrt{91\cdot144-1440}\)
\(=12\cdot9=108\)
a, căn bậc 117,5 mũ 2 - 26,5 mũ 2 - 1440
b căn bậc 146,5 mũ 2 - 109, 5 mũ 2 + 27 nhân 256