help please :)

Question

Perform these operations:

 

A) (√12x^5) - (√18x) - (√300x^5) + (√98x)

 

B) ³√2 {(³√12x) - (³√2x)} 

 

C) (√5 + 2)(6 - √5)

 

D) (2 + 4√5)(3 - 2√5)

 

 

Answer 1

We need to simplify the radicals in each expression.  To do this, we break up the radicals by their factors in such a way that will allow us to cancel out the radicals.

 

Keep this rule in mind:

 

^m√(xⁿ ) = (x)^n/m

 

^m√(x^m) = x

 

 

A)

 

√(12x⁵) - √(18x) - √(300x⁵) + √(98x) =

 

√4 √3 √(x⁴) √x  -  √9 √2 √x  -  √100 √3 √(x⁴) √x  +  √49 √2 √x =

 

2x² √(3x)  -  3√(2x)  -  10x² √(3x)  +  7√(2x)

 

 

Combining like terms, we end up with

 

4√(2x)  -  8x² √(3x)

 

 

Do the same for B.

 

 

For C and D

 

Use FOIL to simplify.