So today we are doing a blog about square roots of imperfect squares. The square root that I was given is the square root of 33. To figure out this square root, you have to think first “What are the two perfect square roots that are closest to 33?” The answer to the question is the square root of 25(which is 5) and the square root of 36(which is 6) you obviously know that the square root of 33 is going to be between 5 and 6.

First, find how many numbers are between 25 and 36.

36-25= 11

Now you know that there are 11 numbers in between 25 and 36. Try to find the middle of 25 and 36.

11/2=5.5

25+5.5=30.5

Since halfway is 30.5 and we are trying to find the square root of 33, we know that the answer will be above 5.5. There are 3 numbers between 33 and 36, there’s also 2.5 numbers in between 30.5(the middle of 25 and 36) and 33. Therefore, we know that the answer is going to be below 5.75. The answer will be below 5.75, but not too far below it.

We now know that the answer is between 5.7 and 5.8.