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a) \(\sqrt{\dfrac{25}{81}.\dfrac{16}{49}.\dfrac{196}{9}}=\sqrt{\dfrac{25}{81}}.\sqrt{\dfrac{16}{49}}.\sqrt{\dfrac{196}{9}}=\dfrac{5}{9}.\dfrac{4}{7}.\dfrac{14}{3}=\dfrac{40}{27}\)
b) \(\sqrt{3\dfrac{1}{16}.2\dfrac{14}{25}.2\dfrac{34}{81}}=\sqrt{\dfrac{49}{16}.\dfrac{64}{25}.\dfrac{196}{81}}=\sqrt{\dfrac{49}{16}}.\sqrt{\dfrac{64}{25}}.\sqrt{\dfrac{196}{81}}=\dfrac{7}{4}.\dfrac{8}{5}.\dfrac{14}{9}=\dfrac{196}{45}\)
c) \(\dfrac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}=\sqrt{\dfrac{640.34,3}{567}}=\sqrt{\dfrac{64.49}{81}}=\dfrac{\sqrt{64}.\sqrt{49}}{\sqrt{81}}=\dfrac{8.7}{9}=\dfrac{56}{9}\)
d) \(\sqrt{21,6}.\sqrt{810}.\sqrt{11^2-5^2}=\sqrt{21,6.810.\left(11^2-5^2\right)}=\sqrt{216.81.\left(11+5\right)\left(11-5\right)}=\sqrt{36^2.9^2.4^2}=36.9.4=1296\)
a) \(\dfrac{40}{27}\)
b) \(\dfrac{196}{45}\)
c) \(\dfrac{56}{9}\)
d) 1296
a) \(\sqrt{\frac{25}{81}\cdot\frac{16}{49}\cdot\frac{169}{9}}\\ =\sqrt{\left(\frac{5}{9}\right)^2\cdot\left(\frac{4}{7}\right)^2\cdot\left(\frac{13}{3}\right)^2}\\ =\sqrt{\left(\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{13}{3}\right)^2}\\ =\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{13}{3}\\ =\frac{260}{189}\)
b) \(\sqrt{3\frac{1}{6}\cdot2\frac{14}{25}\cdot2\frac{34}{81}}\\ =\sqrt{\frac{19}{6}\cdot\frac{64}{25}\cdot\frac{196}{81}}\\ =\sqrt{\frac{19}{6}\cdot\left(\frac{8}{5}\right)^2\cdot\left(\frac{14}{9}\right)^2}\\ =\sqrt{\frac{19}{6}\cdot\left(\frac{8}{5}\cdot\frac{14}{9}\right)^2}\\ =\sqrt{\frac{19}{6}\cdot\frac{112}{45}}\\ =\sqrt{\frac{1064}{135}}\)
Bổ sung câu b :
\(\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}=\sqrt{\frac{49}{16}.\frac{64}{25}.\frac{196}{81}}=\sqrt{\frac{49}{16}}.\sqrt{\frac{64}{25}}.\sqrt{\frac{196}{81}}=\frac{7}{4}.\frac{8}{5}.\frac{14}{9}=\frac{196}{45}\)
\(a,\sqrt{2,5}.\sqrt{30}.\sqrt{48}\)
\(=\sqrt{2,5.30.48}\)
\(=\sqrt{3600}\)
\(=60\)
\(b,\sqrt{\left(\sqrt{3}-2\right)^2}=\sqrt{3}-2\)
\(c,\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}\)
\(=\sqrt{\frac{49}{16}.\frac{64}{25}.\frac{196}{81}}\)
\(=\sqrt{\frac{49}{16}}.\sqrt{\frac{64}{25}}.\sqrt{\frac{196}{81}}\)
\(=\frac{7}{4}.\frac{8}{5}.\frac{14}{9}\)
\(=\frac{196}{45}\)
Đúng ko
a) \(M=\sqrt{4\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{16\left(x-1\right)}\)
\(=2\sqrt{x-1}-3\sqrt{x-1}-4\sqrt{x-1}=-5\sqrt{x-1}\)
b) \(N=\sqrt{25\left(y+4\right)}+\sqrt{36\left(y+4\right)}-2\sqrt{81\left(y+4\right)}\)
\(=5\sqrt{y+4}+6\sqrt{y+4}-18\sqrt{y+4}=-7\sqrt{y+4}\)
c) \(P=\sqrt{y-2}-3\sqrt{64\left(y-2\right)}+4\sqrt{49\left(y-2\right)}\)
\(=\sqrt{y-2}-24\sqrt{y-2}+28\sqrt{y-2}=5\sqrt{y-2}\)
a) \(M=\sqrt{4\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{16\left(x-1\right)}.\)
\(M=\sqrt{4\left(x-1\right)}-\sqrt{9\left(x-1\right)}-\sqrt{16\left(x-1\right)}\)
\(=2\sqrt{x-1}-3\sqrt{x-1}-4\sqrt{x-1}\)
\(=-5\sqrt{x-1}\)
b) \(N=\sqrt{25\left(y+4\right)}+\sqrt{36\left(y+4\right)}-2\sqrt{81\left(y+4\right)}\)
\(N=\sqrt{25\left(y+4\right)}+\sqrt{36\left(y+4\right)}-2\sqrt{81\left(y+4\right)}\)
\(=5\sqrt{y+4}+6\sqrt{y+4}\)
\(=-7\sqrt{y+4}\)
c) \(P=\sqrt{\left(y-2\right)}-3\sqrt{64\left(y-2\right)}+4\sqrt{49\left(y-2\right)}\)
\(P=\sqrt{\left(y-2\right)}-3\sqrt{64\left(y-2\right)}+4\sqrt{49\left(y-2\right)}\)
\(=\sqrt{y-2}-24\sqrt{y-2}+28\sqrt{y-2}\)
\(=5\sqrt{y-2}\)
1:
a: \(\sqrt{25}+\sqrt{49}=5+7=12\)
b: \(\sqrt{121}-\sqrt{81}=11-9=2\)
2: x>-2
=>2x>-4
=>2x+1>-3
=>Với x>-2 thì \(\sqrt{2x+1}\) chưa chắc có nghĩa
3:
a: \(\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}\)
\(=\left|\sqrt{3}-1\right|-\sqrt{3}\)
\(=\sqrt{3}-1-\sqrt{3}=-1\)
b: \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)
\(=\left(3\sqrt{7}-2\sqrt{14}\right)\cdot\sqrt{7}+14\sqrt{2}\)
\(=21-14\sqrt{2}+14\sqrt{2}=21\)
c:
\(\dfrac{\sqrt{27}-\sqrt{108}+\sqrt{12}}{\sqrt{3}}\)
\(=\dfrac{3\sqrt{3}-6\sqrt{3}+2\sqrt{3}}{\sqrt{3}}=3+2-6=-1\)
a: \(=3\sqrt{3}-2\sqrt{3}+4\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)
