simplify square roots

Question

 

 

1.  simplify √a^2/b^5

 

     The sq root symbol encloses the whole fraction

 

       ____________

2.  √a/b ________                

           √a^2/b^2

 

      The first sq root symbol encloses the second sq root

 

 

3.  2√3 + √27 - √1/3

 

        the sq root for 1/3 encloses it completely

 

4.  √1/2 • (√8 + √2)

 

     the sq root for 1/2 encloses it completely

Answer 1

You can place the fraction inside the radical in parenthesis

 

1. √( a² / b⁵ ) = a/ b²√b = (a√b) / b³ 

 

 

2.   

     √(a / b √(a² / b²) = √a / ( ba/ b) = 1

 

3.

    2 √3  + √27  - √1/3 =

 

    2 √3 + 3√3 - 1/√3 = 5 √3 - √3/ 3 = 14√3 / 3 

 

4. 

     √1/2 . ( √8 + √2 ) = √(1/2) . 3 √2 = 3√( 1/2 . 2 ) = 3 

 

 

Answer 2

1.  You basically have the square root of a² and b⁵

     This reduces to:

 

   a

------  = ab^-5/2

 b^5/2

 

2.  I'm not exactly sure what you've written here, but I think you do it like this:

 

First, evaluate the inner square root:

 

 a

---

 b

 

Then you have:

    ______

   / a      a         a

 \/---- . ----   =  ---

     b      b         b

         __       __       ___

3.  2\/3  + 3\/3    - \/1/3

    __      __

5\/3   - \/1/3

 

4.  Evaluate the parentheses first:

   _      __         __      __         _

\/8 + \/ 2  =  2\/2  + \/2  =  3\/2

     _          __

(3\/2 ) * (\/1/2) = 3