Three cubed equals what.
In this problem, we’re being asked to find out the value of this expression. In particular, we need to think about what this little three means. What does it mean when we write a little three next to a number?
Well, here’s what it doesn’t mean. It doesn’t mean that the value of this expression is 33. If it did mean that, we ’d expect the second digit, three, to be just as large as the first one. A small number three means something very different. Something else this doesn’t represent is three times three. So this doesn’t have a value of nine. Instead, a little three written next to a number means that that number has been cubed. And if you’re listening carefully when the question was read out, that’s how the expression was read. Three cubed equals what.
So let’s think about what it means to cube the number three. You may remember what it means to have the number two written by a number, to square it. When we square a number, we multiply it by itself. And so three squared is equal to three times three. And so if we have nine blocks, we know that make a square shape, three rows of three. So the little two when a number is squared refers to the two times that that number appears in a multiplication.
In our expression, the small number is a three, not a two. And so our number appears three times in the multiplication, three times three times three. This is what three cubed means. Let’s work out the value. Three multiplied by three equals nine. Now, we need to multiply that by the last three. Nine multiplied by three equals 27.
Let’s show what we’ve just done using blocks. First, we realised that we needed to multiply our number, three times three times three times three. As we’ve already seen, three times three equals nine. And if we made three more of these shapes, we’d have a cube, three times three times three.
And so we know three cubed equals 27.