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Үндсэн товъёог

# Dimensions of a cube from its volume

## Video transcript

let's say that we had a cube let me draw the cube here so we have a cube and we know that the volume of this cube is equal to 512 cubic centimeters so my question to you is what are the dimensions of this cube so what is what is this length going to be what is this I guess you could say depth and what is this height going to be and we know it's a cube so these are all going to be equal and so like always encourage you to pause the video and try to figure it out well let's call let's call this length X if that's X then this is going to be X and then this is X as well so if the volume is 512 cubic centimeters that means that the that means that x times X times X is going to be equal to 512 is going to be equal to 512 or we could say that X to the third power is equal to 512 or we could say that X is equal to the cube root of 512 so what's the cube root of 512 and the easiest way I can think about doing this if I don't have a calculator is to just try to do a prime factorization of this by hand so that's what I'm going to attempt to do so let's see does 2 go into 512 sure 512 even so this is going to be 2 times let's see 256 yep 2 times 256 256 that's also divisible by 2 that's 2 times 128 which is also divisible by 2 that's 2 times 64 which is also divisible by 2 that's 2 times 32 let's see I can keep going that's 2 times 16 which is 2 times 2 times 8 which is 2 times 4 which is 2 times 2 so 512 that's the same thing as 2 to the let's see you have 1 2 3 4 5 6 7 8 9 that's 2 to the 9th power but what we care about is what times itself times itself is equal what number if I have three of them and I multiply them together get us to 512 and to think about that we could say look I have nine numbers here so let me divide it into three groups so if this is one group and this is the next group and then this is the next group right over here we could say that 512 is the same thing as 2 times 2 times 2 which is 8 times 2 times 2 times 2 which is 8 times 2 times 2 times 2 so 512 is the same thing as 8 to the third power so we could say that we could say that X I'll do it over here X is equal to the cube root of instead of writing 512 instead of writing 512 I could write 8 to the third power now what's the cube root of something to the third power was just going to be this something so X X is going to be equal to 8 so if the volume here is 512 cubic centimeters each dimension is going to be 8 centimeters so X is equal to 8 centimeters this is equal to 8 centimeters I'm just writing the unit's now this is equal to 8 centimeters and we're done but if you didn't know offhand that 8 to the third power is 512 this is a reasonable way of coming to that conclusion anyway hopefully that helped