how do you simplify exponent 3 square root 250

Question

 

 

1. how do you simplify ₃√250 ?

 

I have  ₃√25   x     ₃ √10

 

 

 

2. how do you simplify    √a^2/b^5

 

 

3.  how do you simplify  √a/b√a^2/b^2

 

4.  how do you simplify  2 x √25/16

 

 I have 2 x 5/4

 

thanks

Answer 1

Is 3 the exponent or √250

 

 It is very seldom exponent comes as irrational;

 

   (√250 ) ^{3 = (} 5 √10 ) ^3 = 1250 √10 

 

   Then:

 

   ³√250 =³√ (2 . 5 .5 .5) = ³√2 . √5³ = 5 ³√2