I'm going to answer a slightly different question, which is what I think you were asking:
What two consecutive numbers does [tex]\sqrt{55}[/tex] fall between?
To answer that question, find the closest perfect squares on either side of 55.
What is the closest perfect square less than 55?
What is the closest perfect square greater than 55?
Take the square root of both those numbers and those are the whole numbers [tex]\sqrt{55}[/tex] falls between.
