Question

Đưa thừa số ra ngoài dấu căn:

a) $\sqrt{28 x^{4} y^{2}}$ với $y \leq 0$;

b) $\sqrt{63 a^{2} b^{4}}$ với $a \geq 0$;

c) $\sqrt{147(a-1)^{3}}$;

d) $\sqrt{192(y+2)^{5}}$.

Answer 1

chịu.-.

HT~~~

Answer 2

a, -2x^2y căn 7 

b, ab^2 căn 63 

c, a-1 căn 147a-147

d, y+2 nhân căn [192 nhân (y+2)^3]

 

Answer 3

a)-2x²y√7

b) 3ab²√7

c) 7(a-1)√3(a-1)

d) 8(y+2)²√3(y+2)

Answer 4

a) -2x^2y√7

b) 3ab^2√7

c) 7(a-1)√(3(a-1))

d) 8(y+2)^2√(3(y+2))

Answer 5

a. \(-2x^2\sqrt{7}\)

b. \(3ab^2\sqrt{7}\)

c. \(7\left(a-1\right)\sqrt{3\left(a-1\right)}\)

d. \(8\left(y+2\right)^2\sqrt{3\left(y+2\right)}\)

Answer 6

a)-2x^2ycăn 7

b) 3ab^2căn 7

c) 7(a-1)căn 3(a-1)

d) 8(y+2)^2căn 3(y+2)

 

Answer 7

a) -2x^2y

b) 3ab^2

c) 7(a-1) can 3(a-1)

d) 8(y+2)^2 can 3( y+2)

Answer 8

a) Với \(y\le0\), ta có:

 \(\sqrt{28x^4y^2}=2\left|x^2\right|\left|y\right|\sqrt{7}=-2x^2y\sqrt{7}\)

b) Với \(a\ge0\), ta có:

 \(\sqrt{63a^2b^4}=3\left|a\right|\left|b^2\right|\sqrt{7}=3ab^2\sqrt{7}\)

c) \(\sqrt{147\left(a-1\right)^3}=7\left(a-1\right)\sqrt{3\left(a-1\right)}=7\left(a-1\right)\sqrt{3a-3}\)

d) \(\sqrt{192\left(y+2\right)^5}=8\sqrt{3\left(y+2\right)}\left(y+2\right)^2=8\sqrt{3y+6}\left(y+2\right)^2\)

Answer 9

  

Answer 10

a) \(2x^2y\sqrt{7}\)

b) \(3a\left|b^2\right|\sqrt{7}=3ab^2\sqrt{7}\)

 

Answer 11

a, Với y ≤ 0 ta có :

\(\sqrt{28x^4y^2}\) = 2|x²||y|\(\sqrt{7}\) =\(-2x^2y\sqrt{7}\)

b, Với a ≥ 0 ta có :

\(\sqrt{63a^2b^4}=3\left|a\right|\left|b^2\right|\sqrt{7}=3ab^2\sqrt{7}\)

Answer 12

a)-2x²y√7

b) 3ab²√7

c) 7(a-1)√3(a-1)

d) 8(y+2)²√3(y+2)

Answer 13

a, \(\sqrt{28x^4y^2}=\sqrt{\left(2x^2y\right)^2}.7=2x^2y\sqrt{7}=-2x^2y\sqrt{7}\)

b, \(\sqrt{63a^2b^4=\sqrt{ }\left(3ab^2\right)^2.}7=3ab^2.\sqrt{7}=3ab^2\sqrt{7}\)

c,\(\sqrt{147\left(a-1\right)^3}=\sqrt{\left[7\left(a-1\right)\right]^2.3\left(a-1\right)}=7\left(a-1\right)\sqrt{3\left(a-1\right)}\)

d,\(\sqrt{192\left(y+2\right)^5}=\sqrt{\left[8\left(y+2\right)^2\right]^2}.3\left(y+2\right)=8\left(y+2\right)^2\sqrt{3\left(y+2\right)}\)

Answer 14

a. -2x^2\sqrt{7}−2x27​

b. 3ab^2\sqrt{7}3ab27​

c. 7\left(a-1\right)\sqrt{3\left(a-1\right)}7(a−1)3(a−1)​

d. 8\left(y+2\right)^2\sqrt{3\left(y+2\right)}8(y+2)23(y+2)​
 

Answer 15

A-V28x^4 y^2 = -2x^yV7

B-V63a^2 b^4 = 3ab^2V7

C-V147(a-1)^3 = 7(a-)V3(a-1)

D-V192 ( y + 2) ^5 = 8(y+2)^2 V3(y+2)

Answer 16

a)\(\sqrt{28x^1y^2}\) =\(\sqrt{4.7.\left(x^2\right).y^2}\) = \(\sqrt{2^2.7\left(x^2\right).y^2}\) = \(2x^2\left|y\right|\sqrt{7}\) = \(-2x^2y\sqrt{7}\) 

b)\(\sqrt{63a^2b^4}\) = \(\sqrt{9.7.a^2\left(b^2\right)^2}=\sqrt{3^2.7.a^2\left(b^2\right)^2}=3\left|a\right|b^2\sqrt{7}=3ab^2\sqrt{7}\) 

c) \(\sqrt{147\left(a-1\right)^3}=\sqrt{49.3\left(a-1\right)\left(a-1\right)^2}=\sqrt{7^2.3.\left(a-1\right)\left(a-1\right)^2}=7\left(a-1\right)\sqrt{3\left(a-1\right)}=7\left(a-1\right)\sqrt{3a-3}\) d) \(\sqrt{192\left(y+2\right)^5}=8\sqrt{3\left(y+2\right)}\left(y+2\right)^2=8\sqrt{3y+6}\left(y+2\right)^2\)

Answer 17

a, \(\sqrt{28x^4y^2}\) =\(\sqrt{\left(2x^2y\right)^2.7}\) = 2x²y \(\sqrt{7}\)  = - 2x²y\(\sqrt{7}\) 

b,\(\sqrt{63a^2b^4}\) =\(\sqrt{\left(3ab^2\right)^2.7}\) = 3ab² \(\sqrt{7}\)  = 3ab²\(\sqrt{7}\)

c, \(\sqrt{147\left(a-1\right)^3}\) =\(\sqrt{\left[7\left(a-1\right)\right]^2.3\left(a-1\right)}\) = 7(a-1)\(\sqrt{3\left(a-1\right)}\)

d, \(\sqrt{192\left(y+2\right)^5}\) = \(\sqrt{\left[8\left(y+2\right)^2\right]^2.3\left(y+2\right)}\) =8(y+2)²\(\sqrt{3\left(y+2\right)}\)

Answer 18

a)\(\sqrt{\left(2x^2y\right)^2.7}\) =I2x²yI.\(\sqrt{7}\)=-2x²y.\(\sqrt{7}\)( với y<=0)

b)\(\sqrt{\left(3ab^2\right)^2}.7\)=I3ab²I.\(\sqrt{7}\)=3ab².\(\sqrt{7}\)(với a<=0)

c)\(\sqrt{\left[7\left(a-1\right)\right]^2}.3\left(a-1\right)\)=7(a-1).\(\sqrt{3\left(a-1\right)}\)

d)\(\sqrt{\left[8\left(y+2^{ }\right)^2\right]^2.3\left(y+2\right)}\)=8(y+2).\(\sqrt{3\left(y+2\right)}\)\(\sqrt{7}\)\(\sqrt{7}\)

Answer 19

a, ​​ 
x4y228x4y2

 

28x4y228x4y2

y≤0

 

$y\le$

 

 

   

Answer 20

a) \(\sqrt{28^4y^2}=\sqrt{\left(2^2y\right)^2}.7=\left|2x^2y\right|\sqrt{7}=-2x^2y\sqrt{7}\) (vì y ≤ 0)

b) \(\sqrt{63a^2b^4}=\sqrt{\left(3ab^2\right)^2}.7=\left|3ab^2\right|\sqrt{7}=3ab^2\sqrt{7}\) (vì a ≥ 0)

c) \(\sqrt{147\left(a-1\right)^3}=\sqrt{\left[7\left(a-1\right)\right]^2.3\left(a-1\right)}=7\left(a-1\right)\sqrt{3\left(a-1\right)}\)

\(\sqrt{192\left(y+2\right)^5}=\sqrt{\left[8\left(y+2\right)^2\right]^2}.3\left(y+2\right)=8\left(y+2\right)^2\sqrt{3\left(y+2\right)}\)

\sqrt{28 x^{4} y^{2}}=\sqrt{\left(2 x^{2} y\right)^{2} \cdot 7}=\left|2 x^{2} y\right| \sqrt{7}=-2 x^{2} y \sqrt{7}

Answer 21

a, \(\sqrt{28x^4y^2}=\sqrt{\left(2x^2y\right)^2.7}=2x^2y\sqrt{7}=-2x^2y\sqrt{7}\)  ( vì y < 0 )

b,\(\sqrt{63a^3b^4}=\sqrt{\left(3ab^2\right)^3.7}=3ab^2\sqrt{7}=3ab^2\sqrt{7}\)  (vì a > 0 )

c, \(\sqrt{147\left(a-1\right)^3}=\sqrt{\left[7\left(a-1\right)\right]^2.3\left(a-1\right)}=7\left(a-1\right)\sqrt{3\left(a-1\right)}\)

d, \(\sqrt{192\left(y+2\right)^5}=\sqrt{\left[8\left(y+2\right)^2\right]^2.3\left(y+2\right)}=8\left(y+2\right)^2\sqrt{3\left(y+2\right)}\)

Answer 22

a, Căn 28x^4y^2= căn(2 x^2y)^2.7=|2x^2y| căn 7

     = -2x^2y căn 7

b, Căn 63a^2b^4=căn (3ab^2)^2.7=|3ab^2| căn 7=3ab^2 căn 3

c, Căn 149(a-1)^3= căn [7(a-1)]^2.3(a-1)=7(a-1) căn 3(a-1)

d, Căn 192(y+2)^5= căn [8(y+2)^2]^2.3(y+2)

=8(y+2)^2 căn 3(y+2)

Answer 23

a) = 2x\(^2\)y\(\sqrt{7}\)

b) =3ab\(^2\)\(\sqrt{7}\)

c) =\(\sqrt{3\left(a-1\right)}\)

d) =\(\sqrt{3\left(y+2\right)}\)