Fwd: a number rational or irrational.

[Thaga Sheriff]

If we conjugate it the denominator will get irrational.

Then what is the case for

( 7+ root5 | 7- root 5).

Then what about 5 ^1/3 (power).

Plz explain.

---------- Forwarded message ---------
From: Thaga Sheriff <thagash...@gmail.com>
Date: Sun, 18 Oct 2020, 1:07 pm
Subject: Re: a number rational or irrational.
To: Anand Iyer <anandd...@gmail.com>

If we conjugate it the denominator will get irrational.

Then what is the case for

( 7+ root5 | 7- root 5).

Then what about 5 ^1/3 (power).

Plz explain.

On Sun, 18 Oct 2020, 8:27 am Anand Iyer, <anandd...@gmail.com> wrote:

the square root of a number is irrational since it can't be written as a fraction (p/q), unless the number is a perfect square

the cube root of a number is irrational since it can't be written as a fraction (p/q), unless the number is a perfect cube

...

Now, in some such cases, you will be able to simplify the calculation to get the answer as rational.

will give two such examples.

(3root2)^2 = 9 * 2 = 18

(7 + 3root2) * (7 - 3root2) = 49 - 18 = 31.  because you can apply the formula (a + b)(a - b) = (a^2 - b^2)

On Sunday, October 18, 2020 at 5:08:54 AM UTC+5:30 thagash...@gmail.com wrote:

Is 7+3root2 divided by 4 is a rational or irrational.

and

is 5power1/3 a rational or irrational how do you define it.

plz explain