Question

Why is x^4 the largest perfect square of x^5

Answer 1

Answer:

Step-by-step explanation:

Because x^5 has 5 members. When you group them into 2 members each, there is one x left over. This is most easily seen if you try it with numbers.

The clearest way is to pick something that is not a perfect square to start with.

6 * 6 * 6 * 6 * 6

6^2 is a perfect square. It is grouped into 2 groups. Each one is a 6

So 6^2 = 36. 36 is a perfect square.

You should note that 6 ^3  is not a perfect square. One of the 6s is unmatched and you get a fraction when you square root 6^3.

6 * 6 * 6 = 216. The square root of 216 is 14.697... which goes on forever.

6^4 is a perfect square.

6^4 = 1296 The square root of 1296 is 36.