please help simplifing sq rt problem

Question

 

 

would you please help me simplify and solve

 

 

    √135b^2c^3d  ·  √5b^2d

 

 

 

thankyou

Answer 1

Assuming this is what you meant:

 

√(135b^2c^3d) * √(5b^2d), where * means multiply,

d >= 0 so second radical is not imaginary, and

c >= 0 so first radical is not imaginary;

then the expression can be expanded to:

 

√(135) * √(b^2) * √(c^2) * √(c) * √(d) * √(5) * √(b^2) * √(d)

 

√(3*3*3*5) * √(5) * (√(b^2))^2 * c * √(c) * (√(d))^2

 

√(3*3*3*5*5) * b^2 * c√(c) * d

 

3*5*√(3) * b^2 * c√(c) * d

 

15*√(3) * b^2 * c√(c) * d

 

15 * b^2 * c  * d * √(3c)

Answer 2

  √(135 b^2 c^3 d)  .  √(5 b^2 d =

 

  √( 5. 3^3 b^4 c^3 . d . 5.b^2 .d) =

 

  √ (5^2.  3 ^ 3 . c^3. b^6 . d^2) =

 

  5 . 3 .c . b^2 . d √(3c) =

 

    15c b^2 .d  √(3c)