How to do Division of Radicals

Introduction:
                  Radical numbers are in the form of square root. The square root present in the radical number may be either a cubic root or square root. The radical number is present inside each square root or cubic root. The index number is present outside the each square root or cubic root. For example, `root(3)(4)` is known as the radicals.

Example for How to do Division of Radicals

Example 1: How to divide the following radicals, `1/(sqrt(5) - sqrt(6))` .
Solution:
Step 1: Write the given radicals for division, we get,

`1/(sqrt(5) - sqrt(6))`

Step 2: The next step, for performing division , we have to take the conjugate. That means, the denominator term is taken and the sign of the denominator is changed. Then we have multiply the given radicals in both the numerator and denominator.

`1/(sqrt(5) - sqrt(6))`  `xx`  `(sqrt(5) + sqrt(6))/(sqrt(5) + sqrt(6))`

Step 3: By simplifying the above expression, we get,

`(sqrt(5) + sqrt(6))/(sqrt(5)^2 - sqrt(6)^2)`

`(sqrt(5) + sqrt(6))/(5 - 6)`

`(sqrt(5) + sqrt(6))/ - 1`

= - (  `sqrt(5) + sqrt(6)` )

       = - `sqrt(5)`  - `sqrt(6)`
This is the required solution for the division of radicals.