Answer:
[tex] \sqrt{ \frac{36}{16} } [/tex]
Step-by-step explanation:
A rational number is one that can be expressed as a fraction.
- [tex] \sqrt{ \frac{36}{6} } = \sqrt{6} [/tex]
- sqrt(6) is irrational.
Therefore, top left and right and irrational.
Bottom left:
- [tex] \sqrt{ \frac{36}{16} } = \frac{ \sqrt{36} }{ \sqrt{16} } = \frac{6}{4} = \frac{3}{2} [/tex]
- Very obviously already in a fractional form making it rational.
Bottom right:
- [tex] \sqrt{ \frac{16}{6} } = \frac{ \sqrt{16} }{ \sqrt{6}} = \frac{4}{ \sqrt{6} } = \frac{4 \sqrt{6} }{6} = \frac{2 \sqrt{6} }{3} [/tex]
- We already established that the sqrt(6) is not rational, so this expression is also irrational.
