Question

Show that (3+2 root 2)(3-2 root 2)is not an irrational number

Answer 1

0 answer bcz can be divided

Answer 2

First we have to find the expanded form of (3 + 2√2)(3 - 2√2).

$\Longrightarrow\ (3+2\sqrt{2})(3-2\sqrt{2}) \\ \\ \\ \Longrightarrow\ (3)^2-(2\sqrt{2})^2 \ \ \ \ \ \ \ \ \ \ [\because\ a^2-b^2=(a+b)(a-b)] \\ \\ \\ \Longrightarrow\ 9-8 \\ \\ \\ \Longrightarrow\ 1$

Here the result is 1, which is a rational number, isn't it?

1 can be written as a fraction, means in p/q form, as the following:

1 = 1/1 = 2/2 = 3/3 = 4/4 = 5/5 = 6/6 = 7/7 = 8/8 = 9/9 = 10/10......

Thus, we found that  (3 + 2√2)(3 - 2√2)  is a rational number because it results in 1.

Hence proved that  (3 + 2√2)(3 - 2√2)  is not an irrational number.