Reminder Example about Repeated Multiplying of Square Roots

If `x = sqrt10`, then

`x^2 = (sqrt10)^2 = 10`

[This because square and square root are inverse processes.]

Let's multiply our previous answer by `sqrt10`.

`x^3 = (sqrt10)^3 = (sqrt10)^2sqrt10` ` = 10sqrt10`

The next step in the pattern is:

`x^4 = (sqrt10)^4 = 10 *(sqrt10)^2` ` = 10 × 10 = 100`

[Once again, we are multiplying our previous answer by `sqrt10`.]

The next step in the pattern is:

`x^5 = (sqrt10)^5 = 100sqrt10`

The next step in the pattern is:

`x^6 = (sqrt10)^6 = 1000`

What we are doing next in Powers of j works in the same way.

Please support IntMath!