Question

an irrational number between 3 and 4 in root form​

Answer 1

Answer: The two rational numbers between 3 and 4 are 3.5 and 3.75.

Two irrational numbers between 3 and 4 are √11 and √13.

Step-by-step explanation:

Here, the given numbers are 3 and 4,

Since, both 3 and 4 are rational numbers,

Also, the average of two rational number is also a rational number and it is between the numbers

⇒ A rational number between 3 and 4 = Average of 3 and 4

Now, both 3.5 and 4 are the rational number,

⇒ A rational number between 3.5 and 4 = Average of 3.5 and 4

Thus, the two rational numbers between 3 and 4 are 3.5 and 3.75.

Now, we know that the square root of prime number is always an irrational number.

The squares of 3 and 4 are 9 and 16 respectively.

And, two prime numbers between 9 and 16 are 11, 13

⇒ Two irrational numbers between 3 and 4 are √11 and √13.

Answer 2

Answer:

If a and b are two positive rational numbers such that ab is not a perfect square of a rational number, then

ab

is an irrational number lying between a and b.

So an irrational number between 3 and 4 is=

3×4

=

3

×

4

=

3

×2=2

3