Question

2 root 7 by 7 root 7 is a rational number or irrational number

Answer 1

$\frac{2 \sqrt{7} }{7 \sqrt{7} } \: \: \: \: is \: \: \: rational$
Proof,

$\frac{2 \sqrt{7} }{7 \sqrt{7} } = \frac{2}{7} = 0.285714285714285714$

Where 0.285714285712...... is an recuring decimal expantion so it is rational number.

Answer 2

Given:

2 root 7 by 7 root 7

To find:

The given number is rational or irrational

Solution:

The given number is rational.

We can determine if the given number can be written as p/q and the value of q is unequal to 0.

The given number=2 root 7 by 7 root 7

=2√7/7√7

=2/7

The fraction obtained is 2/7 and the denominator's value is greater than 0.

Since it can be mentioned as p/q, q≠0, we can conclude that it is rational.

Therefore, the given number is rational.