Question

Let is a rational number. Prove that this is irrational number
$\sqrt{7}$
Don't copy to internet. Give the right answer please.

Answer 1

Hiii!!!

Here's Ur answer...

We know numbers which can be represented in the form of p/q and q≠0 are called rational numbers.

There are two types of numbers, which are :-

>> Terminating
>> Non-terminating

Terminating r those numbers which terminates after some decimal expansion and remainder comes 0

Non-terminating are those numbers which never terminates and remainder never comes 0.

In non-terminating numbers, there r two more types :-

1. Repeating
2. Non-repeating

repeating r those numbers whose numbers r repeating in it's Decimal expansion. Like 3.33333333... , 5.67676767... etc

Non-repeating r those numbers whose numbers don't repeat in their decimal expansion. For example :- 6.001000100001.... , 7.46292626282.... etc

Now, which numbers can be represented in the form of p/q and q≠0

Terminating can be represented in the form of p/q and non-terminating repeating numbers can be..

So they are rational number.

Is √7 a rational number??

Is it terminating or non-terminating repeating??

√7 = 2.64575131...

We can clearly see here that it's neither terminating nor repeating. It's a non-terminating non-repeating number. So it's not a rational number, it's irrational.

Hope u understood!!