Question 1

What are the differences between square roots and cube roots?

Accepted Answer

The square root of a number is the number that when you multiply it by itself two times, you get your original number. The _cube_ root is the number that when you multiply it by itself *3* times, you get your original number. For example, the square root of 25 is 5, because 5*5 = 25. The cube root of 64 is 4, because 4*4*4 = 64.
I hope this helps, and I didn't confuse you any more.

Question 2

what is a perfect square and what does it mean? 0:46

Accepted Answer

A perfect square is a number that can be expressed as the product of two equal integers.

Examples of perfect squares:
* 9
o 9 is a perfect square becuase it can be expressed as 3 * 3 (the product of two equal integers)
* 16
o 16 is a perfect square becuase it can be expressed as 4 * 4 (the product of two equal integers)
* 25
o 25 is a perfect square becuase it can be expressed as 5 * 5 (the product of two equal integers)

NON examples of perfect squares:

… (more) * 8
o 8 is a not perfect square because you cannot express it as the product of two equal integers
* 5
o 5 is a not perfect square because it cannot be expressed as the product of two equal integers
* 7
o 7 is a not perfect square because you cannot express it as the product of two equal integers

hope this helps :)

Question 3

at 1:26 what does he mean by "nine of the way through it? Please help

Accepted Answer

Take the distance from 36 to 49.  that difference is 13  (49-36=13)
Next take the distance from 36 to 45. that difference 9.
So when you are going from 36 to 49, you will arrive at 45 at when you have completed nine 16ths of the trip.

Question 4

What is the difference between square roots and cube roots

Accepted Answer

Squaring a number multiplies twice. Some squared numbers:
1² = 1 * 1
2² = 2 * 2
3² = 3 * 3
4² = 4 * 4
5² = 5 * 5
Cubing a number multiplies three times. Some cubed numbers:
1³ = 1 * 1 * 1
2³ = 2 * 2 * 2
3³ = 3 * 3 * 3
4³ = 4 * 4 * 4
5³ = 5 * 5 * 5
And so on.
But when we take the ROOT of a number, what we are actually doing is asking a question. When we get the square root of a number we are asking, "What number times what number equals the number we are squaring?" For example:
√4 = 2
The square root of 4 equals 2. Why? Because 2 times 2 equals 4. Another example:
√9 = 3
The square root of 9 equals 3. Why? Because 3 times 3 equals 9.
Now, the difference between square roots and cube roots is that with cube roots, we are asking a similar question, but the amount that the numbers need to multiply changes.
³√8 = 2
The cube root of 8 equals 2. Why? Because 2 times 2 times 2 equals 8. Another example:
³√27 = 3
The cube root of 27 equals 3. Why? Because 3 times 3 times 3 equals 27.
I hope you were able to understand and get through all that! It was a rather hefty manuscript. :)
Toodleoo! **tips hat**

Question 5

Does anyone know how to square root with a power of 3

Accepted Answer

To square root with a power of three, you will cube root the number.

For example, 4 to the power of three, or 4 squared is the cube root of 64, or 4*4*4.

Question 6

Wouldn't 6 + 9/13 be the square root of 45?

Accepted Answer

This is an interesting question.  It is true that 45 is 9/13 of the way from 36 to 49.  However, because the square root function is a *nonlinear* function, the previous sentence does *not* mean that sqrt(45) is *exactly* 9/13 of the way from sqrt(36)=6 to sqrt(49)=7.

Since the graph of the square root function is concave down, sqrt(45) is *larger* than 6 + 9/13; sqrt(45) is about 6.708, but 6 + 9/13 is only about 6.692.  
Visually, the graph of the function y=sqrt(x) on the interval 36<x<49 is above the graph of the line segment joining (36, 6) and (49, 7) but excluding the endpoints.  This is why it makes sense for sqrt(45) to exceed 6 + 9/13.  So 6 + 9/13 is only an approximation for sqrt(45).

Have a blessed, wonderful day!

Question 7

What does Sal mean when he says "This isn't a linear relationship" at 1:21?

Accepted Answer

Sal means that every time we increase the number inside the sqrt by a constant amount, the value of sqrt(x) doesn't increase by a proportional amount.
For example:
45 - 36  = 9.
sqrt(45) - sqrt(36) is about 0.7.

54 - 45 = 9 (again). 
sqrt(54) - sqrt(45) is about 0.6.

If the relationship was linear, the difference between sqrt(54) and sqrt(45) would be 0.7 again, because in linear relationships the change in one variable is proportional to the change in another. However, the change in the value of sqrt(x) is not the same between x = 45 and x = 54

Question 8

What is a principal square root Sal mentions at 0:20?

Accepted Answer

The principle square root: Have you ever thought of it this way? Lets say you have √25. Now you would obviously automatically know that it is 5, right? But what about -5? You also know that -5 squared is 25 because a negative times a negative is a positive. Therefore, we call the positive square root (5) the principle square root to avoid confusion with the negative one. Hope this helped! :)

Question 9

whats the differences to square roots and cube roots?

Accepted Answer

A square root of a number returns the number which, multiplied by itself, gives the number. Cube root, on the other hand, returns the number which, multiplied by itself thrice, gives the number.

8th grade

Course: 8th grade > Unit 1

Approximating square roots to hundredths

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