Question

Answer 1

^{*Mình tách từng bài ra để giải anh/cj nhé!}

`@` `\text {Ans}`

`\downarrow`

`2,`

`a,`

`\sqrt {225/9} = 15/3` `(15^2 = 255; 3^2 = 9)`

`b,`

`-\sqrt {(-111)^2} = -111 (` `(-111)^2 = 111` `)`

`c,`

`-(\sqrt {1/400})^2 = -1/400` `(\sqrt {1/400} = 1/20; -(1/20)^2 = -1/400)`

`d,`

`(- \sqrt {7/3})^2 = 7/3` 

Answer 2

4:

a: =>x^2=324

=>x=18 hoặc x=-18

b: =>x^2=5/16

=>x=căn 5/4 hoặc x=-căn 5/4

c: =>x-3=1/4

=>x=13/4

d: =>4x+1=9

=>x=2

Answer 3

Bài 2 : 

\(a,\sqrt{\dfrac{225}{9}}=\dfrac{\sqrt{225}}{\sqrt{9}}=\dfrac{\sqrt{15^2}}{\sqrt{3^2}}=\dfrac{15}{3}=5\)

\(b,-\sqrt{\left(-111\right)^2}=-\sqrt{12321}=-\sqrt{111^2}=-111\)

\(c,-\left(\sqrt{\dfrac{1}{400}}\right)^2=-\dfrac{1}{400}\)

\(d,\left(-\sqrt{\dfrac{7}{3}}\right)^2=\sqrt{\left(\dfrac{7}{3}\right)^2}=\dfrac{7}{3}\)

Bài 3 : \(a,\dfrac{2}{5}\sqrt{25}-\dfrac{9}{2}\sqrt{\dfrac{16}{81}}+\sqrt{144}=\dfrac{2}{5}.5-\dfrac{9}{2}.\dfrac{4}{9}+12\)

                                                        \(=2-2+12\)

                                                        \(=12\)

 \(b,0,5\sqrt{0,09}-2\sqrt{0,25}+\sqrt{\dfrac{1}{4}}=0,5.0,3-2.0,5+0,5=0,5.\left(0,3-2+1\right)=0,5.\left(-0,7\right)=-0,35\)

\(c,\sqrt{1\dfrac{9}{16}}-\dfrac{3}{2}\sqrt{\dfrac{64}{9}}=\sqrt{\dfrac{25}{16}}-\dfrac{3}{2}\sqrt{\dfrac{8^2}{3^2}}=\dfrac{5}{4}-\dfrac{3}{2}.\dfrac{8}{3}=\dfrac{5}{4}-4=-\dfrac{11}{4}\)

\(d,-\sqrt{\dfrac{-289}{-16}}+10\sqrt{-\dfrac{-0,09}{9}}\)

\(=-\sqrt{\dfrac{289}{16}}+10\sqrt{\dfrac{0,09}{9}}\)

\(=-\dfrac{17}{4}+10.\dfrac{1}{10}\)

\(=-\dfrac{17}{4}+1\)

\(=-\dfrac{13}{4}\)

Answer 4

`3,`

`a,`

`2/5 \sqrt {25} - 9/2 \sqrt {16/81} + \sqrt {144}`

`= 2/5*5 - 9/2 * 4/9 + 12`

`= 2 - 2 + 12`

`= 12`

`b,`

`0,5 \sqrt {0,09} - 2\sqrt {0,25} + \sqrt {1/4}`

`= 0,5 * 0,3 - 2 * 0,5 + 0,5`

`= 0,15 - 1 + 0,5`

`= -0,35`

`c,`

`\sqrt {1 9/16} - 3/2 \sqrt {64/9}`

`= 5/4 - 3/2*8/3`

`= 5/4 - 4`

`= -11/4`

`d,`

`-\sqrt {-289/-16} + 10` \(\sqrt{-\dfrac{-0,09}{9}}\)

`= -17/4 + 10 * 0,1`

`= -17/4+1`

`= -13/4`

Answer 5

`4,`

`a)`

`-x^2 + 324 =0`

`=> -x^2 = -324`

`=> x^2 = 324`

`=> x^2 = (+-18)^2`
`=> x \in {18; -18}`

`b,`

`16x^2 - 5=0`

`=> 16x^2 = 5`

`=> x^2 = 5/16`

`=> x = \sqrt {5/16}` hoặc `-\sqrt {5/16}`

`c,`

\(\dfrac{2}{\sqrt{x-3}}=4\)

`=> \sqrt {x-3} = 2/4`

`=> \sqrt {x-3} = 1/2`

`=> x-3 = 1/2^2`

`=> x-3 = 1/4`

`=> x=1/4 + 3`

`=> x=13/4`
`d,`

`\sqrt {4x+1} =3`

`=> 4x+1 = 3^2`

`=> 4x+1 = 9`

`=> 4x=8`

`=> x=2`