Question

Find the value of the rationalizing factor of $\sqrt 7 + \sqrt 3 $ ?
A) $\sqrt 7 $
B) $\sqrt 7 - \sqrt 3 $
C) $\sqrt 3 $
D) $\sqrt 7 + \sqrt 3 $

Answer 1

Hint:The rationalizing factor of $\sqrt 7 + \sqrt 3 $ is that number which when multiplied by $\sqrt 7 + \sqrt 3 $ removes all the radicals and gives a rational number. In this question change the sign directly to get the rationalizing factor of the given question.

Complete step-by-step answer:
We know that the rationalizing factor of $\sqrt a + \sqrt b $ is $\sqrt a - \sqrt b $
Hence comparing with 7 and 3 with a and b respectively , we get
The rationalizing factor of $\sqrt 7 + \sqrt 3 $ is $\sqrt 7 - \sqrt 3 $.

Note: When a radical cannot be evaluated , it is called an irrational number. So, in order to rationalize the numerator, we need to get rid of all radicals that are in the numerator . The factor of multiplication by which rationalization is done, is called the rationalizing factor. If the product of two surds is a rational number, then each surd is a rationalizing factor to others.