Question

What is Rationalisation ?
And Rationalising factor !

Rationalise 1/ (8+5√2)

Answer 1

Answer:

1. RATIONALISATION :--

Consider a given number , whose denominator is irrational. Now , suppose we have to make its Denominator rational. So , all the required steps taken to make denominator rational by multiplying numerator n denominator by any particular number is called Rationalisation.

2. Rationalising Factor ( RF ) :--

Suppose the product of any two irrational number , after multiplying comes to be a rational. In this case , all the numbers obtained is called Rationalising Factor ( RF ).

Example :--

1. (a+√b ) , (a-√b ) are RF.
2. (a+b√x ) ,(a-b√x) are RF.
3. (√x+√y) , (√x-√y) are RF.

Rationalise 1/ (8+5√2)

$1 \div (8 + 5 \sqrt{2} ) \\ 1 \div (8 + 5 \sqrt{2} ) \times (8 - 5 \sqrt{2}) \div (8 - 5 \sqrt{2}) \\ (8 - 5 \sqrt{2} ) \div ({8}^{2} - (5 \sqrt{2} ) {}^{2} ) \\ (8 - 5 \sqrt{2} ) \div 14 \: \: \: \: (answer)$