Relating side lengths and areas of squares
About this video
The video finds which two whole numbers the side length of a square with area 45 lies between. Since side x satisfies x^2 = 45, and 45 is between the perfect squares 36 and 49, the side length sqrt(45) is between 6 and 7, and closer to 7.
You'll be able to
- explain that the side length of a square is the square root of its area.
- find which two consecutive whole numbers a square root lies between using perfect squares.
- judge which whole number a square root is closer to.
Key words
- perfect square
- A number you get by multiplying a whole number by itself, like 36 = 6 x 6.
- square root
- The number that multiplied by itself gives a certain value; sqrt(45) is the side of a square with area 45.
- consecutive whole numbers
- Whole numbers that come one right after the other, like 6 and 7.
Transcript
- [Instructor] A square has an area of 45 square units. The side length of this square is between which two consecutive whole numbers? So pause this video and see if you can figure that out. All right. So let's just imagine this. So, if we have this square, and let's say that each side has length X, it's a square, so they're all equal, the area is going to be X times X, or we could say it's X squared, and it's going to be equal to 45.
So let's think about this a little bit. 45 sits between what two perfect squares? If we have, let's see, three squared, four squared, three squared gets us to nine, four squared gets us to 16. See five squared gets us to 25. Six squared gets us to 36. Actually, this is interesting.
So we know that six squared is equal to 36 and that seven squared is equal to 49. So X squared is sitting between six squared and seven squared, and actually it's closer to seven squared. So X is going to sit between six and seven. Another way of thinking about this is that the square root of 45 is between six and seven based on what I just went through.
So that is this choice right here. And it actually would be a little bit, it'd be closer to seven than to six because we can see that it, 45 is a lot closer to 49 than it is to 36, especially on this upper bound. But I'll leave you there.
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