Multiply. Assume that no radicands were formed by raising negative numbers to even powers.

Question

Multiply. Assume that no radicands were formed by raising negative numbers to even powers.

 

(^3√8x - ^3√5y)^2

Answer 1

Convert the radicals to fractional exponents.  ³ √x  is the same as x^1/3.

 

 

[ ³ √(8x)    -   ³ √(5y) ]² =

 

[ (8x)^1/3   -  (5y)^1/3 ]²

 

 

Expand the radical expression.

 

 

[ (8x)^1/3   -  (5y)^1/3 ] * [ (8x)^1/3   -  (5y)^1/3 ] =

 

(8x)^2/3  -  2[ (8x)^1/3 (5y)^1/3 ]  +  (5y)^2/3  =

 

³ √(64x²)  -  2[ ³ √(8x)  ³ √(5y) ]  +  ³ √(25y²)

 

 

Next, break up the radicals by their factors.

 

³ √(64)  ³ √(x²)  -  2[ ³ √(8)  ³ √(x)  ³ √(5)  ³ √(y) ]  +  ³ √(25)  ³ √(y²) =

 

4  ³ √(x²)  -  2[ 2  ³ √(x)  ³ √(5)  ³ √(y) ]  +  ³ √(25)  ³ √(y²) =

 

4  ³√(x²)  -  4   ³√(x)   ³√(5)   ³√(y)   +  ³√(25)   ³√(y²)