Rationalisation is the process of eliminating the irrational numbers from the denominator of a fraction. It is done by multiplying both numerator and denominator by a suitable factor.


The simplest rationalising factor is the smallest possible factor that can be used to eliminate the irrational number from the denominator.


To find the simplest rationalising factor of 5 root 486, we need to follow these steps:

1. Express the given number as a product of its factors.


2. Identify the factors that are perfect squares.


3. Multiply the denominator by the factors that are not perfect squares.


4. Multiply both numerator and denominator by the square root of the perfect square factors.


5. Simplify the expression.

Given: 5 root 486

Step 1: Express the given number as a product of its factors.
5 root 486 = 5 * root (2 x 3 x 3 x 3 x 3 x 3)

Step 2: Identify the factors that are perfect squares.
In this case, there are no perfect square factors.

Step 3: Multiply the denominator by the factors that are not perfect squares.
The denominator is already in its simplest form.

Step 4: Multiply both numerator and denominator by the square root of the perfect square factors.
In this case, there are no perfect square factors.

Step 5: Simplify the expression.
5 root 486 = 5 root (2 x 3^5) = 5 root 2 x 3^2 x 3 root 2 = 30 root 2

Therefore, the simplest rationalising factor of 5 root 486 is 30.