Question

examine, whether the following numbers are rational or irrational 1)(3+√3)(3-√3) ​

Answer 1

Here we have been asked if (3+√3)(3-√3) is a rational or irrational number . But for finding that we need to simplify it .

The simplification is nothing but the answer .

Answer :

→In the attachment←

Steps followed :

• If we observe carefully ; the given problem : (3+√3)(3-√3) is in the form of (a+b)(a-b) identity . Where : → a = 3 → b = √3

• Then ; we took the expansion : a² - b² .

• Then substituted the values of a and b as 3 and √3 .

• Then simplified according to the identity .

• Got the final answer as 6

6 is a rational number .

As it can be written in p by q form where p and q are integers and q is not equal to zero as it can be written as ⁶/₁

So the given expression is a rational number .

Answer 2

Answer:

$(3 + \sqrt{3} )(3 - \sqrt{3} ) \\ \\ = {3}^{2} - { \sqrt{3} }^{2} \\ \\ = 9 - 3 = 6$

HENCE IT IS A RATIONAL NUMBER AS BECAUSE 6 CAN BE WRITTEN AS 6/1.