Project #2: Things are getting rooted
Squares and Roots
02
During this project you will explore how to determine whether a number is a perfect square as well as how to find a square root of any positive number.
Part 1: Reading the leaves
Return to the Den and find where squares and roots do battle together (hint: look at the picture -->). Click on rings of knowledge and read about factor trees. Then go to plant to try a few with a little help when you feel good with factor trees complete these on your own (144, 229, 356, and 576). Now look at the factors if and only if there is an even number of all the prime factors then the number is a perfect square. determine if the numbers you've completed trees for are perfect squares or not.
Example
Not a perfect square
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Perfect Square
Part 2: Digging up the roots
Roots for perfect squares come from separating the prime factors into two of the exact same groups. Multiplying the numbers of one of these groups together provide the square root. When the numbers are not perfect squares then you follow the same procedure but now you will have a third group of factors that there is not a pairing for. These factors stay under the root thus you have a number multiplied by a root as your answer. For an example watch the following video. Now determine the roots of (144, 229, 356, and 576) showing of your work.
Part 3: Testing the water
You know you understand when you can make good estimations. To make an estimation you look at the nearest perfect squares above and below and look at how much closer your number is to the one than the other and guess the whole number of the number below and a decimal of how far you are from that number. Choose 12 numbers at random and provide your reasoning for your estimations then find them using the methods we learned to test your estimations. write these out and email all of the steps to the dragonarch. Email can be sent by clicking the button below