Question

find atlest two irrational number between 2 and 3​

Answer 1

ANSWER:

GIVEN :

Two number 2 and 3

Required to find :

1. Find two irrational numbers between them

Solution :

This question is simple ,

Just we need to about the concept behind it .

For any two given number a and b we can find an irrational number between them using the formula √ab ( this is read as root over the given two numbers).

So,

Let's solve this problem ;

Here is the calculations.

The first number lies between 2 and 3

So, using the above mentioned formula let's try to solve it.

$2 \: and \: 3 \\ = \sqrt{2 \times 3} \\ = \sqrt{6}$

Therefore,

The first irrational number is √6

Similarly ;

Let's find the second number.

The second number lies between 2 and √6

Hence ,

$2 \: and \: \sqrt{6} \\ = \sqrt{2 \times \sqrt{6} } \\ = \sqrt{2 \sqrt{6} } \\ = (2 \sqrt{6} {)}^{ \frac{1}{2} }$

Therefore,

The second irrational number is (2√6)^1/2.

Conclusion:

There will be infinity irrational numbers between any two given numbers.

Answer 2

Helo mate here your ans

The finding an irrational number between two irrational numbers a and b is root ab.

Then irrational number between 2 and 3 =

2×3

=

√6

And other irrational number =

√2×√ 6

= √2×√6