Question

Find the products
Please Solve This​

Answer 1

Step-by-step explanation:

Solution:

Let x =1.8181… …(i)

100x = 181.8181… …(ii) [multiplying eqn. (i) by 100]

99x = 180 [subtracting (i) from (ii)]

x = 18099

Hence, 1.8181… = 18099 = 2011

Solution:

Yes, ‘ab’ is necessarily an irrational.

For example, let a = 2 (a rational number) and b = √2 (an irrational number)

If possible let ab = 2√2 is a rational number.

Now, aba = 22√2 = √2 is a rational number.

[∵ The quotient of two non-zero rational number is a rational]

But this contradicts the fact that √2 is an irrational number.

Thus, our supposition is wrong.

Hence, ab is an irrational number.