# CLASS-8RATIONALIZATION

Rationalization

There is a irrational number suppose a + √b, let us multiply a - √b, and the product of these two irrational numbers would be a rational number. (a + √b) . (a - √b) = a² - (√b)² = a² – b, this process is called Rationalization. We say that, a + √b is the rationalizing factor of a - √b, similarly a - √b is the rationalizing factor of a + √b.

There is an irrational number suppose 5 + √7, let us multiply 5 - √7 and the product of these two irrational numbers would be a rational number. (5 + √7) . (5 - √7) = 5² - (√7)² = 25 – 7 = 18, this process is called rationalization. We say that, 5 + √7 is the rationalizing factor of 5 - √7, similarly 5 - √7 is the rationalizing factor of 5 + √7.

If, a + √b is an irrational number then a - √b is the rationalizing factor of a + √b, similarly a + √b is the rationalizing factor of a - √b.

So, a - √b and a + √b are said to be conjugate to each other.

7

Example. Rationalize the denominator of ----------                                                                                                                                                 5 + √7

7             7             5 - √7

-------- = --------- X ----------

5 + √7       5 + √7         5 - √7

7 (5 - √7)

=  ------------------------

(5 + √7) (5 - √7)

35 - 7√7         35 - 7√7        35 - 7√7

= ------------ = ----------- = -----------

5² - (√7)²         25 – 7             18

35            7√7

= --------- - ---------    (Ans.)

18             18