How Do You Estimate the Square Root of a Non-Perfect Square?

Square some whole numbers and see if we can find one that equals 55
Since there isn't a whole number we can square to get 55, we need to estimate the answer
To see how close our estimate was, we just need to square it and see if it's close to 55
Since 56.25 is pretty close to 55, 7.5 is a good estimate for the square root of 55

1. Remember, to square a number is to multiply it by itself
2. This is the same as taking a number to the second power
1. Perfect squares are the numbers you get when you square an integer
2. So if you take the square root of a perfect square, you get a whole number
1. Since squaring is the opposite of square root, this means 5 is the square root of 25
1. Since squaring is the opposite of square root, this means 6 is the square root of 36
1. Since squaring is the opposite of square root, this means 7 is the square root of 49
1. Since squaring is the opposite of square root, this means 8 is the square root of 64
1. Since we have been trying all the whole numbers in order, this means there must not be a whole number we can square to get 55
1. When we squared 7, we got a number smaller than 55
2. And when we squared 8, we got a number bigger than 64
3. Since there are no whole numbers in between 7 and 8, there must not be a whole number we can square to get 55
4. This means 55 is NOT a perfect square
1. The square root of 55 can't be a whole number
2. But we know it's somewhere in between 7 and 8
1. Since 55 is in between 49 and 64, the numbers we got when we squared 7 and 8, the square root of 55 should be between 7 and 8
2. 7.5 is right in between 7 and 8, so that's a good guess to start with
1. To see how close our estimate was, we just need to square it and see if it's close to 55

What is the square root of 55?