Question

How do you rationalize the denominator and simplify `4/(6-sqrt5)`?

Answer 1

`= (24 + 4 sqrt5)/ (31)`

Explanation:

`4 / ( 6 -sqrt5)`

To rationalize the denominator, we multiply the expression , by the conjugate of the denominator.

Conjugate , of `6 -sqrt5 = color(blue)( 6 + sqrt5`

`4 / ( 6 -sqrt5) = (4 * (color(blue)( 6 + sqrt5))) / (( 6 -sqrt5) * color(blue)( 6 + sqrt5)`

• Applying below mentioned property to simplify denominator:
  `color(blue)((a-b)(a+b) = a^2 - b^2`

`= (4 * (color(blue)( 6)) + 4 * (sqrt5))/ (( 6 ) ^2 -(sqrt5)^2)`

`= (24 + 4 sqrt5)/ ((36 - 5)`

`= (24 + 4 sqrt5)/ (31)`