Question

Bài 32 (trang 19 SGK Toán 9 Tập 1)

Tính

a) $\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}$ ;                              b) $\sqrt{1,44.1,21-1,44.0,4}$ ;

c) $\sqrt{\dfrac{165^2-124^2}{164}}$ ;                                d) $\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}$ .

Answer 1

Giải:

#Học tốt!!!

Answer 2

a) 7 /24

b) 1, 08

c) 17/2

d) 15 /29

Answer 3

916.549.0,01=(1.16+916).(5.9+49).1100

2516.499.1100=2516.499.1100

54.73.110=5.74.3.10

724.

b) $\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}$

$=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}$

$=1,2.0,9=1,08$.

1652−1242164=(165−124)(165+124)164

41.289164=2894

2894=172.

1492−7624572−3842=(149−76)(149+76)(457−384)(457+384)

73.22573.841=225841

225841=1529.

Answer 4

916.549.0,01=(1.16+916).(5.9+49).1100

2516.499.1100=2516.499.1100

54.73.110=5.74.3.10

724.

b) $\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}$

$=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}$

$=1,2.0,9=1,08$.

1652−1242164=(165−124)(165+124)164

41.289164=2894

2894=172.

1492−7624572−3842=(149−76)(149+76)(457−384)(457+384)

73.22573.841=225841

225841=1529.

Answer 5

916.549.0,01=(1.16+916).(5.9+49).1100

2516.499.1100=2516.499.1100

54.73.110=5.74.3.10

724.

b) $\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}$

$=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}$

$=1,2.0,9=1,08$.

1652−1242164=(165−124)(165+124)164

41.289164=2894

2894=172.

1492−7624572−3842=(149−76)(149+76)(457−384)(457+384)

73.22573.841=225841

225841=1529.

Answer 6

Answer 7

a) \(\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{\dfrac{25}{16}.\dfrac{49}{9}.0,01}=\dfrac{5}{4}.\dfrac{7}{3}.0,1=\dfrac{7}{24}\)

b) \(\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44.\left(1,21-0,4\right)}=\sqrt{1,44.0,81}=1,2.0,9=1,08\)

c) \(\sqrt{\dfrac{165^2-124^2}{164}}=\sqrt{\dfrac{\left(165-124\right)\left(165+124\right)}{164}}=\sqrt{\dfrac{41.289}{164}}=\sqrt{\dfrac{289}{4}}=\dfrac{17}{2}\)

d) \(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}=\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}=\sqrt{\dfrac{73.225}{73.841}}=\sqrt{\dfrac{225}{841}}=\dfrac{15}{29}\)

Answer 8

\(a=\dfrac{7}{24};b=1.08;\dfrac{17}{2};\dfrac{15}{29}\)

Answer 9

a) 

Answer 10

a) 

Answer 11

a\(\dfrac{7}{24}\)

b 1,08

c 17/2

d 15/29

Answer 12

a, \(\sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{\dfrac{25}{16}.\dfrac{49}{9}.\dfrac{1}{100}}=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}=\dfrac{5}{4}.\dfrac{7}{3}\dfrac{1}{10}=\dfrac{7}{24}\)

b,\(\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44.\left(1,21-0,4\right)}=\sqrt{1,44.0,81}=\sqrt{144}.\sqrt{0,81}=12.0,9=10,8\)
c,
\(\sqrt{\dfrac{165^2-124^2}{164}}=\sqrt{\dfrac{\left(165-124\right).\left(165+124\right)}{164}}=\sqrt{\dfrac{41.289}{164}}=\sqrt{\dfrac{289}{4}}=\dfrac{\sqrt{289}}{\sqrt{4}}=\dfrac{17}{4}\)
d, \(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}=\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}=\sqrt{\dfrac{73.225}{73.841}}=\sqrt{\dfrac{225}{841}}=\dfrac{\sqrt{225}}{\sqrt{841}}=\dfrac{15}{29}\)

Answer 13

a) \sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{(\dfrac{1.16+9}{16}).(\dfrac{5.9+4}{9}).\dfrac{1}{100}}1169​.594​.0,01​=(161.16+9​).(95.9+4​).1001​​

=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}=\dfrac{\sqrt{25}}{\sqrt{16}}.\dfrac{\sqrt{49}}{\sqrt{9}}.\dfrac{\sqrt{1}}{\sqrt{100}}=1625​​.949​​.1001​​=16​25​​.9​49​​.100​1​​

=\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}=\dfrac{5.7}{4.3.10}=45​.37​.101​=4.3.105.7​

=\dfrac{7}{24}=247​.

b) \sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}1,44.1,21−1,44.0,4​=1,44(1,21−0,4)​

=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}=1,44.0,81​=1,44​.0,8

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Answer 14

a, = \(\sqrt{\dfrac{25}{16}.\dfrac{49}{9}}.\dfrac{1}{100}\) = \(\sqrt{\dfrac{25}{16}}\). \(\sqrt{\dfrac{49}{9}}\) .\(\sqrt{\dfrac{1}{100}}\) = \(\dfrac{\sqrt{25}}{\sqrt{16}}\). \(\dfrac{\sqrt{49}}{\sqrt{9}}\).\(\dfrac{\sqrt{1}}{\sqrt{100}}\) = \(\dfrac{5}{4}\) . \(\dfrac{7}{3}\) .\(\dfrac{1}{10}\)= \(\dfrac{35}{120}\)=\(\dfrac{7}{24}\)

b, = \(\sqrt{1,44}.\left(1,21-0,4\right)\) = \(\sqrt{1,44}.0,8\) = \(\sqrt{\dfrac{144}{100}.\dfrac{81}{100}}\) = \(\sqrt{\dfrac{144}{100}}\).\(\sqrt{\dfrac{81}{100}}\)= \(\dfrac{\sqrt{144}}{\sqrt{100}}\).\(\dfrac{\sqrt{81}}{\sqrt{100}}\)

= \(\dfrac{12}{10}\). \(\dfrac{9}{10}\) =\(\dfrac{108}{100}\)=\(\dfrac{27}{25}\)

c, = \(\sqrt{\dfrac{\left(165-124\right).\left(165+124\right)}{164}}\)= \(\sqrt{\dfrac{41.289}{164}}\)= \(\sqrt{\dfrac{289}{4}}\)=\(\dfrac{\sqrt{289}}{\sqrt{4}}\)=\(\dfrac{17}{2}\)

d, = \(\sqrt{\dfrac{\left(149-76\right).\left(149+76\right)}{\left(457-384\right).\left(457+384\right)}}\)=\(\sqrt{\dfrac{73.225}{73.841}}\)=\(\sqrt{\dfrac{225}{841}}\)=\(\dfrac{\sqrt{225}}{\sqrt{841}}\)=\(\dfrac{15}{29}\)

Answer 15

916.549.0,01=(1.16+916).(5.9+49).1100

2516.499.1100=2516.499.1100

54.73.110=5.74.3.10

724.

b) $\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}$

$=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}$

$=1,2.0,9=1,08$.

1652−1242164=(165−124)(165+124)164

41.289164=2894

2894=172.

1492−7624572−3842=(149−76)(149+76)(457−384)(457+384)

73.22573.841=225841

225841=1529.

Answer 16

Answer 17

Answer 18

a) \sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{(\dfrac{1.16+9}{16}).(\dfrac{5.9+4}{9}).\dfrac{1}{100}}1169​.594​.0,01​=(161.16+9​).(95.9+4​).1001​​

=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}=\dfrac{\sqrt{25}}{\sqrt{16}}.\dfrac{\sqrt{49}}{\sqrt{9}}.\dfrac{\sqrt{1}}{\sqrt{100}}=1625​​.949​​.1001​​=16​25​​.9​49​​.100​1​​

=\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}=\dfrac{5.7}{4.3.10}=45​.37​.101​=4.3.105.7​

=\dfrac{7}{24}=2

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Answer 19

Answer 20

.

Answer 21

a) = 7/24

b) = 27/25

c) = 17/2

d) = 15/29

Answer 22

916.549.0,01=(1.16+916).(5.9+49).1100

2516.499.1100=2516.499.1100

54.73.110=5.74.3.10

724.

b) $\sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}$

$=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}$

$=1,2.0,9=1,08$.

1652−1242164=(165−124)(165+124)164

41.289164=2894

2894=172.

1492−7624572−3842=(149−76)(149+76)(457−384)(457+384)

73.22573.841=225841

225841=1529.

Answer 23

Answer 24

a,\(\dfrac{7}{24}\)

b,1,08

c,\(\dfrac{17}{2}\)

d,\(\dfrac{15}{29}\)

Answer 25

a) \sqrt{1\dfrac{9}{16}.5\dfrac{4}{9}.0,01}=\sqrt{(\dfrac{1.16+9}{16}).(\dfrac{5.9+4}{9}).\dfrac{1}{100}}1169​.594​.0,01​=(161.16+9​).(95.9+4​).1001​​

=\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}=\dfrac{\sqrt{25}}{\sqrt{16}}.\dfrac{\sqrt{49}}{\sqrt{9}}.\dfrac{\sqrt{1}}{\sqrt{100}}=1625​​.949​​.1001​​=16​25​​.9​49​​.100​1​​

=\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}=\dfrac{5.7}{4.3.10}=45​.37​.101​=4.3.105.7​

=\dfrac{7}{24}=247​.

b) \sqrt{1,44.1,21-1,44.0,4}=\sqrt{1,44(1,21-0,4)}1,44.1,21−1,44.0,4​=1,44(1,21−0,4)​

=\sqrt{1,44.0,81}=\sqrt{1,44}.\sqrt{0,81}=1,44.0,81​=1,44​.0,81

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Answer 26

a)\(\dfrac{7}{24}\)

b)\(1,08\)

c)\(\dfrac{17}{2}\)

d)\(\dfrac{15}{29}\)

Answer 27

 

Answer 28

a) \(\sqrt{1\dfrac{9}{16}\cdot5\dfrac{4}{9}\cdot0,01}\)

= \(\sqrt{\left(\dfrac{1\cdot16+9}{16}\right)\cdot\left(\dfrac{5\cdot9+4}{9}\right)\cdot\dfrac{1}{100}}\)

= \(\sqrt{\dfrac{25}{16}}\cdot\sqrt{\dfrac{49}{9}}\cdot\sqrt{\dfrac{1}{100}}\)

= \(\dfrac{\sqrt{25}}{\sqrt{16}}\cdot\dfrac{\sqrt{49}}{\sqrt{9}}\cdot\dfrac{\sqrt{1}}{\sqrt{100}}\)

= \(\dfrac{5}{4}\cdot\dfrac{7}{3}\cdot\dfrac{1}{10}\)

= \(\dfrac{7}{24}\)

b) \(\sqrt{1,44\cdot1,21-1,44\cdot0,4}\)

= \(\sqrt{1,44.\left(1,21-0,4\right)}\)

= \(\sqrt{1,44\cdot0,81}\)

= \(\sqrt{1,44}\cdot\sqrt{0,81}\)

= 1,2 . 0,9 

= 1,08

c) \(\sqrt{\dfrac{165^2-124^2}{164}}\)

= \(\sqrt{\dfrac{\left(165-124\right)\left(165+124\right)}{164}}\) 

= \(\sqrt{\dfrac{41\cdot289}{164}}\) = \(\sqrt{\dfrac{289}{4}}\) = \(\dfrac{\sqrt{289}}{\sqrt{4}}\) = \(\dfrac{17}{2}\)

d) \(\sqrt{\dfrac{149^2-76^2}{457^2-384^2}}\)

= \(\sqrt{\dfrac{\left(149-76\right)\left(149+76\right)}{\left(457-384\right)\left(457+384\right)}}\)

\(\sqrt{\dfrac{73\cdot225}{73\cdot841}}\) = \(\sqrt{\dfrac{225}{841}}\) = \(\dfrac{\sqrt{225}}{\sqrt{841}}\) = \(\dfrac{15}{29}\)

 

Answer 29

\(\sqrt{\dfrac{1.16+9}{16}.\dfrac{5.9+4}{9}.\dfrac{1}{100}}\)      =\(\sqrt{\dfrac{25}{16}}.\sqrt{\dfrac{49}{9}}.\sqrt{\dfrac{1}{100}}\)            =\(\dfrac{5}{4}.\dfrac{7}{3}.\dfrac{1}{10}\) =\(\dfrac{7}{24}\)                                                                  b)\(\sqrt{1,44\left(1,21-0,4\right)}=\sqrt{1,44}.0,81\)

Answer 30

a, \(\dfrac{7}{24}\)   ;b= 1,08  ;c=\(\dfrac{17}{2}\)   ;d=\(\dfrac{15}{29}\)