# Rationalising the Denominators

Consider an example,, we can rationalize this by multiplying and dividing value of the denominator.

Â´ =

Now, consider a rational number of the form.

Let us do this problem step by step.

Step (1)

Take LCM of the denominators.

=

Step (2)

Multiply the numerator and then the denominator.

=

Step (3)

Simplify the expression.

Hence,

Â

Let us take another problem.

Let us rationalize the denominator and simplify the given expression.

First, take the conjugate of the denominator.

=

Now, multiply the numerators and the denominators.

Â

Simplify the expression.

=

We can simplify a value without changing the given value. This can be done using rationalisation. We apply this rationalisation to eliminate the radicals without changing the value.

We know that the rational numbers are closed, commutative and distributive for addition and multiplication. The irrational number also satisfies the commutative, associative, and distributive laws for addition and subtraction.