Answer:
The number which is a rational number is:
[tex]\sqrt{\dfrac{36}{16}}[/tex]
Step-by-step 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)
[tex]\sqrt{\dfrac{36}{6}}[/tex]
It could be written as:
[tex]\sqrt{6}[/tex]
As the number inside the square root is not a whole square term hence the number is not a rational number.
4)
[tex]\sqrt{6}[/tex]
As done above.
The given number is not a rational number.
3)
[tex]\sqrt{\dfrac{16}{6}}[/tex]
This number could also be written as:
[tex]\sqrt{\dfrac{16}{6}}=\sqrt{\dfrac{8}{3}}[/tex]
which could again be written in simplified form as:
[tex]2\sqrt{\dfrac{2}{3}}[/tex]
As the square root term is retained in the expression.
Hence, this number is not a rational number.
2)
[tex]\sqrt{\dfrac{36}{16}}[/tex]
This number could also be written as:
[tex]\sqrt{\dfrac{9}{4}}=\sqrt{(\dfrac{3}{2})^2}=\dfrac{3}{2}[/tex]
As we could see that the number could be easily expressed in the form of p/q.
Hence, the number is a rational number.
