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.
September 15, 2014 at 3:12 pm
Rylee, your thinking here is awesome! I really like it. On the last section… You said sq root of 33 is 2.5 numbers away from sq root of 30.5. How far away is sq root of 33 from sq root of 36? It appears to me that sq root of 33 is actually closer to sq root of 30.5 (5.5) than it is to sq root of 36 (6). I would guess somewhere between 5.7 and 5.75. Sq root of 33 is going to be pretty close to 5.75, but not over 5.75. What do you think?