Question

Bài 28 (trang 18 SGK Toán 9 Tập 1) 

Tính

a) $\sqrt{\dfrac{289}{25}}$ ;                       b) $\sqrt{2\dfrac{14}{25}}$ ;

c) $\sqrt{\dfrac{0,25}{9}}$ ;                     d) $\sqrt{\dfrac{8,1}{16}}$.

Answer 1

a, \(\sqrt{\frac{289}{25}}=\frac{\sqrt{289}}{\sqrt{25}}=\frac{17}{5}\)

b, \(\sqrt{2\frac{14}{25}}=\sqrt{\frac{64}{25}}=\frac{8}{5}\)

c, \(\sqrt{\frac{0,25}{9}}=\frac{\sqrt{0,25}}{\sqrt{9}}=\frac{0,5}{3}=\frac{1}{2}.\frac{1}{3}=\frac{1}{6}\)

d, \(\sqrt{\frac{8,1}{16}}\)đề có sai ko cô ? 

Answer 2

a) căn 289 / 225 = 17/15

b) căn 64/ 25 = 8/5

c) căn 0,25 / 9 = 1/6

d) căn 8,1 / 1,6 = 9/4

Answer 3

289225=289225=1715.

1425=2.25+1425=6425=6425=85.

0,259=0,259=0,53=530=16.

8,11,6=8116=8116=94.

Answer 4

289225=289225=1715.

1425=2.25+1425=6425=6425=85.

0,259=0,259=0,53=530=16.

8,11,6=8116=8116=94.

Answer 5

289225=289225=1715.

1425=2.25+1425=6425=6425=85.

0,259=0,259=0,53=530=16.

8,11,6=8116=8116=94

 

Answer 6

a)\(\sqrt{\dfrac{289}{25}}=\dfrac{\sqrt{289}}{\sqrt{25}}=\dfrac{17}{5}\)

b)\(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{28}{25}}=\dfrac{\sqrt{4}\cdot\sqrt{7}}{\sqrt{25}}=\dfrac{2\cdot\sqrt{7}}{5}\)

c)\(\sqrt{\dfrac{0,25}{9}}=\dfrac{\sqrt{0,25}}{\sqrt{9}}=\dfrac{0,5}{3}\)

d)\(\sqrt{\dfrac{8,1}{16}}=\dfrac{\sqrt{8,1}}{\sqrt{16}}=\dfrac{\sqrt{8,1}}{4}\)

Answer 7

 

Answer 8

Bài giải câu a;\(\sqrt{\dfrac{289}{25}}\)\(=\)\(\dfrac{\sqrt{285}}{\sqrt{25}}\)\(=\dfrac{17}{5}\)

Bài giải câu b;\(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{64}{25}}=\dfrac{\sqrt{64}}{\sqrt{25}}=\dfrac{8}{5}\)

Bài giải câu c;\(\sqrt{\dfrac{0,25}{9}}=\dfrac{\sqrt{0,25}}{\sqrt{9}}=\dfrac{1}{6}\)   Bài giải câu d;\(\sqrt{\dfrac{8,1}{16}}=\dfrac{\sqrt{8,1}}{\sqrt{16}}=\)\(\dfrac{9}{4}\)

Answer 9

a) \(\sqrt{\dfrac{289}{25}}=\dfrac{17}{5}\)

b) \(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{2.25+14}{25}}=\sqrt{\dfrac{64}{25}}=\dfrac{8}{5}\)

c) \(\sqrt{\dfrac{0,25}{9}}=\dfrac{0,5}{3}=\dfrac{5}{30}=\dfrac{1}{6}\)

d) \(\sqrt{\dfrac{8,1}{16}}=\sqrt{\dfrac{81}{160}}=\dfrac{9}{4\sqrt{10}}\)

Answer 10

a) 17/5             b) 8/5                c) 0,5/3                 d) 

Answer 11

a)\(\sqrt{\dfrac{289}{25}}=\dfrac{\sqrt{289}}{\sqrt{25}}=\dfrac{17}{5}\)

b)\(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{28}{25}}=\dfrac{\sqrt{28}}{\sqrt{25}}=\dfrac{2\sqrt{7}}{5}\)

c)\(\sqrt{\dfrac{0,25}{9}}=\sqrt{\dfrac{1}{\dfrac{4}{9}}}=\sqrt{\dfrac{1}{4}:9}=\sqrt{\dfrac{1}{4}}:\sqrt{9}=\dfrac{1}{2}:9=\dfrac{1}{18}\)

d)\(\sqrt{\dfrac{8,1}{16}}=\sqrt{\dfrac{81}{\dfrac{10}{16}}}=\sqrt{\dfrac{81}{10}:16}=\sqrt{\dfrac{81}{10}}:\sqrt{16}=\dfrac{9\sqrt{10}}{10}:4=\dfrac{9\sqrt{10}}{40}\)

Answer 12

\(\dfrac{17}{15};\dfrac{8}{5};\dfrac{1}{6};\dfrac{9}{4}\)

Answer 13

\(\dfrac{17}{5}\), \(\dfrac{8}{5}\),\(\dfrac{0.5}{3}\), \(\dfrac{9\sqrt{10}}{40}\)

Answer 14

\(\sqrt{12+2\sqrt{35}}\)

=\(\sqrt{2^2.3+2^2.35}\)

=\(2\sqrt{3+35}\)

=\(2\sqrt{38}\)  = \(\sqrt{2^2.38}\)

=\(\sqrt{2^2.2^2.3^2}\)     = \(\sqrt{2^2}.\sqrt{2^2}.\sqrt{3^2}\)

=\(2.2.3\) = 12

Answer 15

Answer 16

Answer 17

a)\(\sqrt{}\)289/225=\(\sqrt{}\)289/225=17/15

b)   \(\sqrt{}\)2/14/25=\(\sqrt{}\)2.25+14/25=\(\sqrt{}\)64/25=\(\sqrt{}\)64/25=5/8

c)   \(\sqrt{}\)0,25/9=\(\sqrt{}\)0,25/9=0,5/3=3/50=1/6

d) \(\sqrt{}\)8,1/1,6=\(\sqrt{}\)81/16=\(\dfrac{\sqrt{ }}{\sqrt{ }}\)81/16=\(\dfrac{9}{4}\)

Answer 18

.

 

289225=289225=1715.

1425=2.25+1425=6425=6425=85.

0,259=0,259=0,53=530=16.

8,11,6=8116=8116=94.

 

 

Answer 19

289225=289225=1715.

1425=2.25+1425=6425=6425=85.

0,259=0,259=0,53=530=16.

8,11,6=8116=8116=94.
 

Answer 20

a, \(\dfrac{\sqrt{289}}{\sqrt{25}}=\dfrac{17}{5}\)

b, \(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{64}{25}}=\dfrac{\sqrt{64}}{\sqrt{25}}=\dfrac{8}{5}\)

c, \(\sqrt{\dfrac{0,25}{9}}=\dfrac{\sqrt{0,25}}{\sqrt{9}}=\dfrac{0,5}{3}\)

d, \(\sqrt{\dfrac{8,1}{16}}=\dfrac{\sqrt{8,1}}{\sqrt{16}}=\dfrac{9\sqrt{10}}{40}\)

Answer 21

a, \(\sqrt{\dfrac{289}{25}}=\dfrac{\sqrt{289}}{\sqrt{25}}=\dfrac{17}{5}\)

b, \(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{64}{25}}=\dfrac{\sqrt{64}}{\sqrt{25}}=\dfrac{8}{5}\)

c,\(\sqrt{\dfrac{0,25}{9}}=\dfrac{\sqrt{0,25}}{\sqrt{9}}=\dfrac{0,5}{3}=\dfrac{1}{6}\)

d,\(\sqrt{\dfrac{8,1}{16}}=\dfrac{\sqrt{81}}{\sqrt{160}}=\dfrac{9}{4\sqrt{10}}=\dfrac{9\sqrt{10}}{40}\)

Answer 22

Answer 23

a,\(\sqrt{\dfrac{289}{225}}=\sqrt{\dfrac{289}{225}}=\dfrac{17}{15}\)

b,\(\sqrt{2\dfrac{14}{25}}=\sqrt{\dfrac{2.25+14}{25}}=\sqrt{\dfrac{64}{25}}=\dfrac{\sqrt{64}}{\sqrt{25}}=\dfrac{8}{5}\)

c,\(\sqrt{\dfrac{0,25}{9}}_{ }=\dfrac{\sqrt{0,25}}{\sqrt[]{9}}=\dfrac{0,5}{3}=\dfrac{5}{30}=\dfrac{1}{6}\)

d,\(\sqrt{\dfrac{8,1}{1,6}}=\sqrt{\dfrac{81}{16}}=\dfrac{\sqrt{81}}{\sqrt{16}}=\dfrac{9}{4}\)

Answer 24

a, \(\sqrt{\dfrac{289}{25}}\)=\(\sqrt{^{ }285}\) /\(\sqrt{25}\) = \(\dfrac{17}{15}\) 

b\(\sqrt{2\dfrac{14}{25}}\)=  \(\sqrt{\dfrac{64}{25}}\)= \(\sqrt{64}\) / \(\sqrt{25}\) = \(\dfrac{8}{5}\) 

c\(\sqrt{\dfrac{0,25}{9}}\) = \(\sqrt{\dfrac{25}{900}}\) = \(\sqrt{25}\) /\(\sqrt{900}\) =\(\dfrac{5}{30}\) 

d \(\sqrt{\dfrac{8,1}{1,6}}\) =\(\sqrt{\dfrac{81}{16}}\) = \(\sqrt{81}\) / \(\sqrt{16}\) =\(\dfrac{9}{4}\)

Answer 25

a) 

Answer 26

Answer 27

Answer 28

Answer 29

sử dụng định lý: với số a,b không âm b\(\ne\)0 , ta có;

\(\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\)

cách đổi hỗn số ra phân số:

\(a\dfrac{b}{c}=\dfrac{a\cdot c+b}{c}vớic\ne0\)

a,\(\sqrt{\dfrac{289}{225}}=\dfrac{\sqrt{289}}{\sqrt{225}}=\dfrac{17}{15}\)

b,\(2\sqrt{\dfrac{14}{25}}=\sqrt{\dfrac{2\cdot25+14}{25}}=\sqrt{\dfrac{64}{25}}=\dfrac{\sqrt{64}}{\sqrt{25}}=\dfrac{8}{5}\)

c,\(\sqrt{\dfrac{0,25}{9}}=\dfrac{\sqrt{0,25}}{\sqrt{9}}=\dfrac{0,5}{3}=\dfrac{5}{30}=\dfrac{1}{6}\)

d,\(\sqrt{\dfrac{8,1}{1,6}}=\sqrt{\dfrac{81}{16}}=\dfrac{\sqrt{81}}{\sqrt{16}}=\dfrac{9}{4}\)

 

Answer 30