Question

What is the procedure to rationalise the denominator?

Answer 1

For good understanding, Let's take an example.

Let an irrational number is $\frac{a+\sqrt{b}}{a-\sqrt{b}}$

here, numerator is $a+\sqrt{b}$
and denominator is $a-\sqrt{b}$

first of all, multiply and divide by numerator in given irrational number.

e.g., $\frac{a+\sqrt{b}}{a-\sqrt{b}}\times\frac{a+\sqrt{b}}{a+\sqrt{b}}$

now resolve the expression,

$\frac{(a+\sqrt)(a+\sqrt{b})}{(a-\sqrt{b})(a+\sqrt{b})}$

= $\frac{(a+\sqrt{b})^2}{a^2-\sqrt{b}^2}$

= $\frac{a^2+\sqrt{b}^2+2a\sqrt{b}}{a^2-b}$

=$\frac{a^2+b+2a\sqrt{b}}{a^2-b}$

now you see, denominator (a² - b) is a rational number , hence it is complete rationalize.so, you just follow the above steps and use algebraic formula to resolve the expression.

Answer 2

Answer:

Step-by-step explanation: The process to rationalise the denominator

1. To rationalise the denominator, you need to multiply  both numerator and denominator  by the radicals in the denominator

2 . Simplify the radicals

3. Reduce the fraction  in the lowest form if it possible.

Here is some example

4/1 +√7

to rationalise the denominator

= 4 / 1+ √7 × ( 1- √7)/(1- √7)

= 4 - 4√7/1-√49

= 4- 4 √7/ 1-7

= 4-4√7/ -6

= -2 ( -2 + 2√7) / -6

= -2 + 2√7 /3