Looking for Pythagoras- Math Reflection Quesions Investigation 2

1. Describe how you would find the length of a line segment connecting two dots on dot paper. Be sure to consider horizontal, vertical, and tilted segments. 

          Horizontal: 

          Vertical:

          Titled: 

There are two strategies for this:

1. You could get a ruler and measure the line segment or you could count the units between the two dots that make up the line segment. This may be accurate in some instances, like when the line is perfectly straight and the measurement ends at a whole number, but sometimes this strategy is inaccurate and hard to get the exact answer with.  

2. You could use the "square method." So you would first have to picture that that line segment is one of the four side of a square. Then, you would draw in the other three sides of the square. To do this, you use the slop of the segment or also known as the "rise over run". After creating a square based off of the simple line segment you would find the area of this square. I have already answered how to find the area in my investigation 1 set of question, but as a quick reminder, you you cut  up the shape into smaller triangles or squares and then add their area's up, or you could draw a bigger square around the square and take away all the excesses pieces from the total area of the bigger square. After finding the area of the shape, all you have to do to find the length of the segment (which is one of the sides of the shape) is find the square root of the area of the shape. 

2. 

a) Explain what it means to find the square root of a number. 
          When you find the square root of a number, you are finding the number that when multiplied by itself, creates the number you are find the square root of. For example, suppose we are trying to figure out the square root of 25. Well, we know that 5*5= 25. So 5 is the square root of 25. As another example, suppose a square has the area of 16 units. Since a square has 4 equal sides, an integer of the length of on of the sides of the square multiplied by itself will come to the total area of the square. The length of the sides of the square is the square root of the area of the square. Coming back to our example, we find out that each of the sides of the square are 4 units long. And since there are four sides to the square which each 4 units long, we can add them all up: 4+4+4+4=16. This proves that the length of the sides of the square is 4 each, as the area adds up correctly. aThis brings us to our final conclusion that the square root of 16 is 4. 

b) Explain whether or not a number can have more than one square root. 
          Yes, a number can have more than one square root. Since, the square of a number is when you multiply  a number by itself to get the digit wanted. For example, take the number 36. The obvious square root is 6. I got my answer as when you multiply 6 by 6, you get 36. However, there is more than just one square root for the square root of 36. The second square root for 36 is -6. The logical behind this answer is that when you multiply two negative integers your answer will always positive. So, -6 multiplied by itself is 36 also. So when writing questions on finding the square root of a number you must specify if you want a negative or positive number. In conclusion, a number can have more than one square root. 

3.

a) Explain what it means to find the cube root of a number.

          To find the cube root of a number is similar to finding the square root of a number. In math, to "cube" something means to times it to the power of the three. So to find the the cube root of a number, you multiply the number by itself three times.  For example to find the cube root of 2 you would perform this equation; 2*2*2=8, Therefore, the cube root of 8, is 2/ 2 cubed is 8.

b) Explain whether or not a number can have more than one cube root.

           A number cannot have more than one cube root. The reason I say this is because, you cannot have a negative number multiplied by itself three times and equal a positive number.  For example, the cube root of 8 is 2, but that doesn't mean the cube root of 8 is also negative 2.  Because -2*-2*-2, equals -8.  Therefore, you can only have one cube root per number.