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) $\sqrt{\genfrac{}{}{0ex}{}{25}{81}\cdot \genfrac{}{}{0ex}{}{16}{49}\cdot \genfrac{}{}{0ex}{}{196}{9}}$

$=\sqrt{\genfrac{}{}{0ex}{}{25}{81}}\cdot \sqrt{\genfrac{}{}{0ex}{}{16}{49}}\cdot \sqrt{\genfrac{}{}{0ex}{}{196}{9}}$

$=\sqrt{{\left(\genfrac{}{}{0ex}{}{5}{9}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{4}{7}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{14}{3}\right)}^2}$

$=\genfrac{}{}{0ex}{}{5}{9}\cdot \genfrac{}{}{0ex}{}{4}{7}\cdot \genfrac{}{}{0ex}{}{14}{3}=\genfrac{}{}{0ex}{}{40}{27}$.

b) $\sqrt{3\genfrac{}{}{0ex}{}{1}{16}\cdot 2\genfrac{}{}{0ex}{}{14}{25}\cdot 2\genfrac{}{}{0ex}{}{34}{81}}$

$=\sqrt{\genfrac{}{}{0ex}{}{49}{16}\cdot \genfrac{}{}{0ex}{}{64}{25}\cdot \genfrac{}{}{0ex}{}{196}{81}}$

$=\sqrt{\genfrac{}{}{0ex}{}{49}{16}}\cdot \sqrt{\genfrac{}{}{0ex}{}{64}{25}}\cdot \sqrt{\genfrac{}{}{0ex}{}{196}{81}}$

$=\sqrt{{\left(\genfrac{}{}{0ex}{}{7}{4}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{8}{5}\right)}^2}\cdot \sqrt{{\left(\genfrac{}{}{0ex}{}{14}{9}\right)}^2}$

$=\genfrac{}{}{0ex}{}{7}{4}\cdot \genfrac{}{}{0ex}{}{8}{5}\cdot \genfrac{}{}{0ex}{}{14}{9}=\genfrac{}{}{0ex}{}{196}{45}$.

c) $\genfrac{}{}{0ex}{}{\sqrt{640}\cdot \sqrt{34,3}}{\sqrt{567}}=\sqrt{\genfrac{}{}{0ex}{}{640.34,3}{567}}=\sqrt{\genfrac{}{}{0ex}{}{64.343}{567}}$

$=\sqrt{\genfrac{}{}{0ex}{}{64.49.7}{81.7}}=\sqrt{\genfrac{}{}{0ex}{}{64.49}{81}}$

$=\genfrac{}{}{0ex}{}{\sqrt{64}\cdot \sqrt{49}}{\sqrt{81}}=\genfrac{}{}{0ex}{}{8.7}{9}$

$=\genfrac{}{}{0ex}{}{56}{9}$.

d) $\sqrt{21,6}\cdot \sqrt{810}\cdot \sqrt{11^2-5^2}$

$=\sqrt{21,6.810\cdot \left(11^2-5^2\right)}$

$=\sqrt{216.81.(11+5)(11-5)}$

$=\sqrt{36.6.9^2\cdot 4^2.6}$

$=\sqrt{36^2.9^2\cdot 4^2}=36.9.4=1296$.

a)

\(M=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

\(=\sqrt{4+4\sqrt{5}+5}-\sqrt{4-4\sqrt{5}+5}\)

\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)

\(=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|\)

\(=2+\sqrt{5}-\left(\sqrt{5}-2\right)\) (vì \(2+2\sqrt{5}>0;2-\sqrt{5}< 0\) )

\(=2+\sqrt{5}-\sqrt{5}+2\\ =4\)

b)

\(N=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

\(=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)

\(=\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|\)

\(=\sqrt{7}-1-\left(\sqrt{7}+1\right)\) (vì \(\sqrt{7}-1>0;\sqrt{7}+1>0\) )

\(=\sqrt{7}-1-\sqrt{7}-1\\ =-2\)

a)2

b)-0,4

c)7

a) \(\sqrt{25-9}\) = \(\sqrt{16}\) = 4

b) \(\sqrt{0,01}-\sqrt{0,25}\) = 0,1 - 0,5 =  -0,4

c)\(\sqrt{2.2^2+4^2}+5^2\) = \(\sqrt{2.4+16+25}\) = \(\sqrt{8+16+25}\) = \(\sqrt{49}\) = 7

a: Ta có: \(\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}-11\right)\)

\(=\left(3\sqrt{6}-3+2\sqrt{6}+4-12-4\sqrt{6}\right)\left(\sqrt{6}-11\right)\)

\(=\left(\sqrt{6}-11\right)\left(\sqrt{6}-11\right)\)

\(=127-22\sqrt{6}\)

b: Ta có: \(\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)

\(=\left(1-\sqrt{5}\right)\left(-1-\sqrt{5}\right)\)

=-1+5

=4

1