The Department of Mathematics Education. EMAT 6700 J. Wilson

Math 1: Numbers and Operations


The student will understand and use square roots of positive numbers.

The Pythagorean Theorem and the Area of a Square are two topics that students have been exposed to prior to 9th grade. In order to develop student's understanding of square roots, it is important to build on their prior experiences. Below, we have described one method of constructing the square root of a number. This will aid in student's understanding by connecting to skills that are important in the real-world.

How to measure the square root of a number that can be written as the sum of two squares:

Step 1: Express n as the sum of two squares

(i.e. or ).

Step 2: On a coordinate grid, plot (a, 0) and (a, b).

Step 3: Construct the segment from (a, 0) to (a, b).

Note, this segment has length .

Step 4: Construct a circle with the center (0, 0) and radius of .

The point of intersection of the circle and the x-axis is (, 0).

Consider the following example:

Step 1:


Step 2:

Step 3:


Step 4:

Step 5: (red segment)


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This was designed by Scott Burrell and Kimberly Young