Question

Find an irrational number between 6 and 7​

Answer 1

It is well known fact that

a<ab−−√<ba<ab<b

Now as here 6*7=42 is not a perfect squre , √42 is an irrational number. So √42 is the required irrational.

……..

Again you may think in this way .

6² = 36

7² = 49

Then if x is such that. 36<x<49 then √X is iraational between 6 and 7.

( This concept can be generalized as the above like if a²<x<b² then (√x) is irrational number between a and b if x is not a perfect square)

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Answer 2

Answer:

The correct answer to this question is $\sqrt{42}$

Step-by-step explanation:

Given - An irrational number

To Find - Find an irrational number between $6$ and $7$

Now, we have $6$ × $7$ = $42$

$\sqrt{42}$  is an irrational number ​

irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there is no number among integers and fractions that equals Square root of√2

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