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Lesson 7: Evaluating expressions word problems

# Evaluating expressions with variables: cubes

Discover how to calculate the total surface area of cube-shaped containers with varying side lengths. Learn the formula 6x², where x represents the side length of a cube. Apply this formula to find the surface area of multiple cubes, and add the results to determine the combined surface area that needs painting. Created by Sal Khan.

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• What does ^ mean ?
• The carat is normally used to indicate an exponent. For instance, x^2 is x to the power of 2, or x squared. x^3 is x to the power of 3 or x cubed.
• Because my region, I usually use the sign "," (coma) to denote decimal numbers. I can't figure out if the dot confuses me because I'm unfamiliarizated with it, or it really can be pretty problematic. For instance, does anyone else confuses the expression that shown in the video "1.5²" with "1 times 5²"?
By the way, I'm sorry for my terrible english grammar.
• Andres,
Your English grammar is almost perfect.

It is quite understandable that the "." (period) causes confusion in regions that use the "," (comma) as a decimal point. If I tried to do math using the "," (comma) as the decimal point instead of the "." (period), I would be very confused.

I try to use the "*" (asterisk) as a multiplication symbol because it is less likely to cause confusion. You can also use the "•" (dot) for multiplication, but it is harder to type on most keyboards.
• so how come he didnt make it 2 to the third power
• Sal didn't make it 2^3 because the formula states that to find the surface area of a cube, you do 6(x^2). Now think about it, let's say that you have a regular, 2D square. The side lengths are all 6cm. The formula to find the area is x^2. You would get 6^2=36cm^2. You would not, however, do x^3. The formula to finding the surface area of a cube is only slightly different than that of finding the area of a square.
• How does 1.5 x 2 = 2.5. I'm confuse can you please explain more.
• 1.5*2 is not 1.5 squared. 1.5*1.5 is 1.5 sqaured
• Which word phrase could correspond to the variable expressions n/8?
• The quotient of n divided by 8 = n/8
One-eighth of n = n/8
n things shared among 8 people = n/8
how many 8's in n = n/8
ratio of n and 8 = n/8
All of the above phrases correspond to n/8
8 times a number is n. what is the number?
All the above correspond to n/8
• Why is the formula 6x^2, rather than 11x^2 or 7x^2?
• x^2 gives the area of one side of a cube. The 6 is in there because a cube has 6 sides.
• Before allowing the video to play I made cubes a, and b selecting the length of one side of each, squaring it, adding them together, then multiplying by six. Thus my equation was
a^2 + b^2 (6)
My question is, will doing it this way cause me problems later on down the road?
• This will not work... You are missing a set of parentheses. Your version only multiplies b^2 with the 6. You need to write it as: 6(a^2 + b^2) or (a^2 + b^2) 6 or 6a^2 + 6b^2.
• Isn't The Measurement In Cenimeters
• Or often in Geometry, you will just see the measurement as "units" where you normally see cm, ft, etc.
• How to solve simultaneous equations with two positive signs e.g. 9a+b=13 3a+b=20 Or.
5a+b=27
a+b=7