Can someone help me understand the following in terms that i can understand because i've read the book,definitions i've done research and i am new with this and i still don't understand.The teacher is hopeless at explaining that's why i am here for help.
1) What are the difficulties of understanding radical expressions? How 2) what are square roots? can somone explain it to me in easy words to understand.
3) What are cube roots?
4) what are i believe this is how you write it n^th root
5) what are radicals?
these concepts?
6)What are some limitations of square root?
thank you i figured it out
Let me answer questions 2 and 3 anyway...even if you did figure it out. This answer may help others and may help you have a better understanding of why we call it a 4^3 "four cubed" and why we call 4^2 "four squared."
In Montessori, we have something called the Bead Cabinet. You can see a picture of one here:
http://i23.ebayimg.com/02/i/06/15/ea/10_1.JPG
It is made up of beads (hence the name...) Sometimes, you will hear the work refered to as a "bead chain" because it consists of beads that are put together in a chain. The small three chain looks like this (each "o" would be a bead and each "-" is a link that links them together):
ooo-ooo-ooo
We have a set of plastic arrows to go with this. There are 3 of them. One says 3, the other says 6, and the last one says 9.
The child can count the beads and put the right number at each break. So it will look like this when they are done:
ooo-ooo-ooo
3 6 9
There are 3 sets of 3's...which is 9. 3x3 is 9. OR 3 squared is 9. Why call it 3 squared though? We can take the chain and fold it so it looks like this:
ooo-ooo
ooo
Then fold it again so it looks like this:
ooo
ooo
ooo
Well...close to it. It will actually make a square (rather than a rectangle). So it really IS a "3 square" They just counted it up and know that there are 9 beads. So now they know that 3 squared is 9.
With cubes, we link three of the three chains together (those are what you see hanging in the picture). So they look like this:
ooo-ooo-ooo---ooo-ooo-ooo---ooo-ooo-ooo
The child learns how to count it out (arrows are provided for 3, 6, 9, 12...up to 27) then fold it properly so it looks like this:
ooo-ooo-ooo
ooo-ooo-ooo
ooo-ooo-ooo
Notice how it's 3 of the three squares? Now, go back to the picture of the bead frame again. You can see what the 10 squares and the 9 squares look like fairly decently. (Hard to see 3 just because of the angle of the picture). But if you take the 3 "three squares" we have and stack them on top of each other, we have the same thing as the three cube (see the cubes along the top of the bead frame?) So you usually just have to ask the child, after they did this, "how much is 3 cubed?" They'll look and say "27."
They might not have it memorized or be able to put it in exponential form (3^3), but they understand the concept of it. And, if I explained it well (hard to do without the materials actually in front of you to show you), I hope you do too :)
Matt
1) The difficulties of understanding radical expressions can vary depending on the individual, but some common challenges include:
- Complex notation: The symbols used in radical expressions, such as the square root symbol (√), can be unfamiliar and confusing at first.
- Abstract concept: Radical expressions involve finding the roots or fractional powers of numbers, which can be a difficult concept to grasp.
- Lack of visual representation: Without visual aids or concrete examples, understanding the meaning and purpose of radical expressions can be challenging.
- Mathematical background: If you are new to math or have not yet learned about exponents and roots, understanding radical expressions can be especially difficult.
To overcome these difficulties, it is helpful to break down the concept step-by-step and use visual aids or real-world examples to make the idea more tangible and relatable. Asking for clarification or seeking additional resources from teachers or online tutorials can also be beneficial in understanding radical expressions.
2) Square roots are a type of radical expression that involves finding the number that, when multiplied by itself, gives a specific value. In simpler terms, the square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3 because 3 times 3 equals 9.
To find the square root of a number, you can use various methods such as estimation, prime factorization, or using a calculator. Estimation involves finding the closest perfect square number that is less than or equal to the given number and then guessing the square root. Prime factorization involves breaking down the number into its prime factors and then identifying pairs of the same factors to simplify the square root. Lastly, a calculator can give you the exact value of the square root.
Understanding square roots can be made easier by using visual aids, such as a number line or a square grid, to demonstrate the relationship between the square root and the original number. Exploring real-world examples, like finding the side length of a square or the distance between two points, can also help in understanding the practical applications of square roots.