Rationalising the Denominator:

To rationalize the denominator means to eliminate any radical expressions from the denominator of a fraction, so that the denominator contains only rational numbers (numbers that can be expressed as a ratio of integers).

Method of Rationalisation:

There are two methods of rationalizing the denominator:

1. Rationalizing with conjugates
2. Rationalizing with factors

Rationalizing with Conjugates:

To rationalize a denominator with conjugates, we multiply the numerator and denominator by the conjugate of the denominator. To find the conjugate, we change the sign of the radical expression in the denominator.

For example, to rationalize the denominator of the fraction 1/√6 - √5, we would multiply the numerator and denominator by the conjugate of the denominator, which is √6 + √5.

This gives us:

1/√6 - √5 x (√6 + √5)/(√6 + √5)

Simplifying the numerator and denominator gives us:

(√6 + √5)/(6 - 5)

= √6 + √5

Rationalizing with Factors:

The method of rationalizing with factors involves finding factors of the denominator that will eliminate any radical expressions. For example, to rationalize the denominator of the fraction 1/√2 + 1, we would multiply the numerator and denominator by the conjugate of the denominator, which is √2 - 1.

This gives us:

1/(√2 + 1) x (√2 - 1)/(√2 - 1)

Simplifying the numerator and denominator gives us:

(√2 - 1)/(2 - 1)

= √2 - 1

Answer is = √6 - √5 because when we put 1/√6 - √5 we exactly remove the one from n for rationalize