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a) \(\frac{\sqrt{640}\sqrt{34,3}}{\sqrt{567}}\)
\(= \frac{\sqrt{64.10}\sqrt{49.\frac{7}{10}}}{\sqrt{81.7}}\)
\(= \frac{\sqrt{64}\sqrt{10}\sqrt{49}\sqrt{\frac{7}{10}}}{\sqrt{81}\sqrt{7}}\)
\(= \frac{\sqrt{64}\sqrt{49}}{\sqrt{81}} . \frac{\sqrt{10}\sqrt{\frac{7}{10}}}{\sqrt{7}}\)
\(= \frac{8.7}{9} . \frac{\sqrt{10 . \frac{7}{10}}}{\sqrt{7}}\)
\(= \frac{56}{9} . \frac{\sqrt{7}}{\sqrt{7}}\)
\(= \frac{56}{9} . 1 = \frac{56}{9}\)
b) \(\sqrt{21,6}\sqrt{810}\sqrt{11^2−5^2}\)
\(= \sqrt{216.\frac{1}{10}}\sqrt{81.10}\sqrt{(11−5)(11+5)}\)
\(= \sqrt{36.6.\frac{1}{10}}\sqrt{81}\sqrt{10}\sqrt{6.16}\)
\(= \sqrt{36}\sqrt{6}\sqrt{\frac{1}{10}}\sqrt{81}\sqrt{10}\sqrt{6}\sqrt{16}\)
\(= (\sqrt{36}\sqrt{81}\sqrt{16}).(\sqrt{6}\sqrt{6}).(\sqrt{\frac{1}{10}}\sqrt{10})\)
\(= (6.9.4).\sqrt{6.6}.\sqrt{\frac{1}{10}.10}\)
\(= (54.4).\sqrt{36}.\sqrt{1}\)
\(= 216.6.1 = 1296\)
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) \(\sqrt{21,6}.\sqrt{810}.\sqrt{11^2-5^2}=\sqrt{21,6.810.\left(11^2-5^2\right)}=\sqrt{216.81.\left(11+5\right)\left(11-5\right)}=\sqrt{36^2.9^2.4^2}=36.9.4=1296\)
\(a,\sqrt{2,5}.\sqrt{30}.\sqrt{48}\)
\(=\sqrt{2,5.30.48}\)
\(=\sqrt{3600}\)
\(=60\)
\(b,\sqrt{\left(\sqrt{3}-2\right)^2}=\sqrt{3}-2\)
\(c,\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}\)
\(=\sqrt{\frac{49}{16}.\frac{64}{25}.\frac{196}{81}}\)
\(=\sqrt{\frac{49}{16}}.\sqrt{\frac{64}{25}}.\sqrt{\frac{196}{81}}\)
\(=\frac{7}{4}.\frac{8}{5}.\frac{14}{9}\)
\(=\frac{196}{45}\)
Đúng ko
a) \(\dfrac{40}{27}\)
b) \(\dfrac{196}{45}\)
c) \(\dfrac{56}{9}\)
d) 1296
a) \sqrt{\dfrac{25}{81} \cdot \dfrac{16}{49} \cdot \dfrac{196}{9}}8125⋅4916⋅9196
=\sqrt{\dfrac{25}{81}} \cdot \sqrt{\dfrac{16}{49}} \cdot \sqrt{\dfrac{196}{9}}=8125⋅4916⋅9196
=\sqrt{\left(\dfrac{5}{9}\right)^{2}} \cdot \sqrt{\left(\dfrac{4}{7}\right)^{2}} \cdot \sqrt{\left(\dfrac{14}{3}\right)^{2}}=(95)2⋅(74)2⋅(314)2
=\dfrac{5}{9} \cdot \dfrac{4}{7} \cdot \dfrac{14}{3}=\dfrac{40}{27}=95⋅74⋅314=2740.
b) \sqrt{3 \dfrac{1}{16} \cdot 2 \dfrac{14}{25} \cdot 2 \dfrac{34}{81}}3161⋅22514⋅28134
=\sqrt{\dfrac{49}{16} \cdot \dfrac{64}{25} \cdot \dfrac{196}{81}}=1649⋅2564⋅81196
=\sqrt{\dfrac{49}{16}} \cdot \sqrt{\dfrac{64}{25}} \cdot \sqrt{\dfrac{196}{81}}=1649⋅2564⋅81196
=\sqrt{\left(\dfrac{7}{4}\right)^{2}} \cdot \sqrt{\left(\dfrac{8}{5}\right)^{2}} \cdot \sqrt{\left(\dfrac{14}{9}\right)^{2}}=(47)2⋅(58)2⋅(914)2
=\dfrac{7}{4} \cdot \dfrac{8}{5} \cdot \dfrac{14}{9}=\dfrac{196}{45}=47⋅58⋅914=45196.
c) \dfrac{\sqrt{640} \cdot \sqrt{34,3}}{\sqrt{567}}=\sqrt{\dfrac{640.34,3}{567}}=\sqrt{\dfrac{64.343}{567}}567640⋅34,3=567640.34,3=56764.343
=\sqrt{\dfrac{64.49 .7}{81.7}}=\sqrt{\dfrac{64.49}{81}}=81.764.49.7=8164.49
=\dfrac{\sqrt{64} \cdot \sqrt{49}}{\sqrt{81}}=\dfrac{8.7}{9}=8164⋅49=98.7
=\dfrac{56}{9}=956.
d) \sqrt{21,6} \cdot \sqrt{810} \cdot \sqrt{11^{2}-5^{2}}21,6⋅810⋅112−52
=\sqrt{21,6.810 \cdot\left(11^{2}-5^{2}\right)}=21,6.810⋅(112−52)
=\sqrt{216.81 .(11+5)(11-5)}=216.81.(11+5)(11−5)
=\sqrt{36.6 .9^{2} \cdot 4^{2} .6}=36.6.92⋅42.6
=\sqrt{36^{2} .9^{2} \cdot 4^{2}}=36.9 .4=1296=362.92⋅42=36.9.4=1296.
\(\left(2\sqrt{5}.\sqrt{2}-3\sqrt{40}+\sqrt{90}:3\right):\sqrt{640}=\left(2\sqrt{10}-6\sqrt{10}+\sqrt{10}\right):\left(8\sqrt{10}\right)\)
\(=-\frac{3\sqrt{10}}{8\sqrt{10}}=-\frac{3}{8}\)
C : \(0,2.\sqrt{\left(-10\right)^2.3}+2\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}=10.0,2\sqrt{3}+2l\sqrt{3}-\sqrt{5}l=2\sqrt{3}+2\sqrt{5}-2\sqrt{3}=2\sqrt{5}\)
a/ \(\frac{56}{9}\)
b/ \(1296\)