 In this video, we're going to look at square, cube and triangular numbers, what they are, how they can be useful and some of the patterns they form. A square number is the result of multiplying an integer by itself. A process known as squaring. For example, 4 times 4 equals 16. So 16 is a square number. They are called square numbers because these particular numbers of objects can be arranged in a perfect solid square. They are useful for dealing with quadratics, simplifying surds and in area. See if you can list the first 10 square numbers. Pause and try now. How did you do? In a multiplication table, they are found by going diagonally from top left to bottom right. The nth term of a square number is simple. It's just n squared. They link with both cube and triangular numbers and we'll see how soon. Cube numbers are similar to square numbers in that they are the product of the same integer. However, a cube number is that integer multiplied by itself three times or cubed. For example, 2 times 2 times 2 equals 8. So 8 is a cube number. They are called cube numbers because like the square numbers, they can form a perfectly filled cube shape. The nth term of a cube sequence is again a simple one, n to the power of 3. In maths, they appear often in graphing and iterations, but mostly in topics like volume. Can you list the first 10 cube numbers? Be warned, this is trickier than before. Pause the video and have a go. How did you do? Our final look is at triangular numbers. A triangle number is the number of objects you can arrange in a perfectly filled equilateral triangle. Another way to look at this is each time you increase the number, you increase the previous gap by 1. 1 to 3 has a gap of 2. 3 to 6 has a gap of 3. 6 to 10 has a gap of 4 and so on. You can imagine this by stacking equilateral triangles. For example, the first triangular number is 1 with the row of triangles. The second triangular number has two rows, giving three triangles. The third number needs three rows, so give six triangles and so on. See if you can work out the remaining first 10 triangular numbers. The nth term for finding a triangular number is n to the power of 2 plus n divided by 2. You can find this because the triangular numbers are a quadratic sequence. See this video here for more information. Now for the clever bit. If you look carefully, between the colored triangles are white triangles, the opposite way round. If you count all these triangles, you get another sequence of numbers. 1, 4, 9, 16. Familiar? Yes, these are square numbers again. You can also see triangle and square numbers together in this pattern. If you count alternating colors exactly, you get triangular numbers. If you count the total, you guessed it, square numbers. So there you have the basics of square, cube and triangular numbers.