Answer:
312 lies between perfect squares 289 and 324
None of the options is correct
Step-by-step explanation:
A perfect square is a number that can be expressed as the product of two equal integers. For example, 16 is a perfect square since it can be expressed as [tex]4*4 or 4^{2}[/tex]
We can list a couple of perfect squares and see which option is correct.
[tex]10^{2} = 100[/tex]
[tex]11^{2} = 121[/tex]
[tex]12^{2} = 144[/tex]
[tex]13^{2} = 169[/tex]
[tex]14^{2} = 196[/tex]
[tex]15^{2} = 225[/tex]
[tex]16^{2} = 256[/tex]
[tex]17^{2} = 289[/tex]
312 lies here
[tex]18^{2} = 324[/tex]
[tex]19^{2} = 361[/tex]
Then, we can conclude that
[tex]289 = 17^{2} \leq 312 \leq 18^{2} = 324[/tex]
