Write the perfect root less than and the perfect root greater than the root given. What is the value of the perfect roots?

From the given picture, we can note that
[tex]3=\sqrt[]{9}<\sqrt[]{12}<\sqrt[]{25}=5[/tex]Similarly,
[tex]10=\sqrt[]{100}<\sqrt[]{193}<\sqrt[]{144}=12[/tex]In the same way, we have
[tex]7=\sqrt[]{49}<\sqrt[]{50}<\sqrt[]{121}=11[/tex]and finally,
[tex]9=\sqrt[]{81}<\sqrt[]{93}<\sqrt[]{100}=10[/tex]