# Which #3# digit number is both a square and a cube?

##### 2 Answers

#### Answer:

#### Explanation:

Let

Then

#### Answer:

#### Explanation:

One way to approach this is to consider the cubes and see which meet the other conditions.

There are 3 cubes which are also square numbers, but only

Note that

Their cubes are therefore both squares and cubes.

We could also have started with integers which are cubes, and then square them:

The cubes are:

However, if we look at the indices:

Find the numbers which are sixth powers and have