Question

Which number is a rational number

Answer 1

the one on the bottom right corner with just the 6 in it.

Answer 2

The number which is a rational number is:

`\sqrt{(36)/(16)}`

Explanation:

We know that a rational number is a number than can be expressed in the form of:

p/q

where p is an integer and q is a rational number.

1)

`\sqrt{(36)/(6)}`

It could be written as:

`√(6)`

As the number inside the square root is not a whole square term hence the number is not a rational number.

4)

`√(6)`

As done above.

The given number is not a rational number.

3)

`\sqrt{(16)/(6)}`

This number could also be written as:

`\sqrt{(16)/(6)}=\sqrt{(8)/(3)}`

which could again be written in simplified form as:

`2\sqrt{(2)/(3)}`

As the square root term is retained in the expression.

Hence, this number is not a rational number.

2)

`\sqrt{(36)/(16)}`

This number could also be written as:

`\sqrt{(9)/(4)}=\sqrt{((3)/(2))^2}=(3)/(2)`

As we could see that the number could be easily expressed in the form of p/q.

Hence, the number is a rational number.