Rationalize the following expression 1/(4³√a^2-6³√a^3√b+9³√b^2) Show complete solution and explain the answer.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You need to change the mid term such that 6`root(3)(a^3)* sqrt b`  to become `6 root(3)(a)*root(3)(b)`

The denominator is now changed into `4 root(3)(a^2) - 6 root(3)(a)*root(3)(b) + 9 root(3)(b^2)` .

Multiplying the denominator by `2 root(3)(a) + 3 root(3) (b)`  yields the difference of cubes 8a + 27b.

1/`(4 root(3)(a^2) - 6 root(3)(a)*root(3)(b) + 9 root(3)(b^2))` =`(2 root(3)(a) + 3 root(3) (b))/((4 root(3)(a^2) - 6 root(3)(a)*root(3)(b) + 9 root(3)(b^2))*(2 root(3)(a) + 3 root(3) (b)))`

`1/(4 root(3)(a^2) - 6 root(3)(a)*root(3)(b) + 9 root(3)(b^2))`  =`(2 root(3)(a) + 3 root(3) (b))/(8a+27b)`

Rationalizing the given expression yields `(2 root(3)(a) + 3 root(3) (b))/(8a+27b)` .

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial