Embedded Files
What are Cube and Square Roots?
What are Cube and Square Roots?
In Unit 1.4 & 1.5 we learned and explored cube and square roots. We learned that square roots and cube roots are not just exponents. In fact, saying that something is squared or that something is cubed is very different than asking what the square or cube root of something is.
Square Roots
Square Roots
A square root is the side dimension of a square. So say that you have an area of 49 in a square, what is the side dimension of that square? The side dimension is 7 because in that square each side has 7 squares, if you have four sides with 7 squares instead of having to count each individual square to get the area, you could just multiply 7 by 7 to get the area. Another way to think of it is the side dimension of the square times itself will equal the area of the square. When learning about square roots we used cheez-its (hence the image) to help us better understand what a square root is.
Cube Roots
Cube Roots
A cube root is the side dimension of a cube. To cube something is another way of saying raising something to the third power. An example- you would take 5, multiply it by 5, which equals 25, and then multiply 25 by 5, which equals 125. The cube root of 125 would be 5. During this lesson we experimented on a website where we could rotate a cube of any size and number. This helped us to better understand the concept of cube roots. Here is the link to the website click here to view.
What is a perfect square?
What is a perfect square?
A perfect square is any square where the square root is a counting number. A counting number is every whole number except for zero. So by saying this, if you have an area of 16 and you are trying to find the side dimension of your area you are essentially trying to find the square root of 16 which is 4 because the side length of the square is 4. This would be a perfect square because 4 is a counting number.
An example:
An example:
4²= 16 because 4x4= 16. the square root of 16 would be 4. √16=4
4²= 16 because 4x4= 16. the square root of 16 would be 4. √16=4
The exponents and square root debate.
The exponents and square root debate.
Why do we say "squared" and "cubed" instead of being raised to the third power or second power? Saying that something is being raised to a certain power is called using exponents to learn more about exponents click here to view fellow Pre- Algebra student Kaya's MiMOW blog. When using exponents you have a range of almost any and every number. The reason why we say squared and cubed is simply to help us understand the exponent of 3 and 2 better. It is to help us understand that raising something to the second power would be the same as finding the area of a square. The same goes for cube roots, raising something to the third power would be the same as finding the height, width, and length of a cube.
How are Cube and Square Roots Similar and Different?
How are Cube and Square Roots Similar and Different?
Similar
Similar
Cube and square roots are very similar in that they are both a form of exponents. In order to figure out certain cube root problems you need to know about square roots. Really, cube roots are square roots with more dimension. When doing cube and square roots you are essentially doing the same problem except in cube roots you add one more step.
Different
Different
The real difference between cube and square roots is that cube roots are a far more complicated version of square roots. In fact, when trying to figure out square and cube roots, while you may be using the same steps, cube roots are sometimes much harder to figure out because they are much larger numbers.
A quick summary...
A quick summary...
I find cube and square roots to be very interesting and fun. Many professions use them on a daily basis. Such as: interior designers, architects, engineers, and, well... math teachers! Square and cube roots are used fairly frequently in math and are very practical and useful concepts to know about. I really enjoy cube and square roots and learning about these valuable and practical mathematical concepts.
Page updated
Report abuse