Question

are irrational numbers in 2 rational numbers​

Answer 1

Answer:

Find two irrational numbers between two given rational numbers. Addition of irrational number with any number results into an irrational number. So, x + √2 is an irrational number which exists between two rational numbers a and b.

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Answer 2

Answer:

Let x be the irrational number between two rational numbers 2 – √3 and 5 – √3. Then we get,

2 – √3 < x < 5 – √3

⇒ 2 < x + < √3 < 5

We see that x + √3 is an irrational number between 2 – √3 and 5 – √3 where 2 – √3 < x < 5 – √3.

2. Find two irrational numbers between two given rational numbers.

Now let us take any two numbers, say a and b. Let x be any number between a and b. Then,

We have a < x < b….. let this be equation (1)

Now, subtract √2 from both the sides of equation (1)

So, a – √2 < x < b – √2……equation (2)

= a < x + √2 < b

Addition of irrational number with any number results into an irrational number. So, x + √2 is an irrational number which exists between two rational numbers a and

Step-by-step explanation:

I gave a example tooo