Question

How do you simplify `sqrt(x^11)+sqrt(x^5)`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite this as:

`sqrt(x^10 * x) + sqrt(x^4 * x)`

Next, we can use this rule for radicals to simplify each of the terms:

`sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))`

`sqrt(color(red)(x^10) * color(blue)(x)) + sqrt(color(red)(x^4) * color(blue)(x)) =>`

`(sqrt(color(red)(x^10)) * sqrt(color(blue)(x))) + (sqrt(color(red)(x^4)) * sqrt(color(blue)(x))) =>`

`x^5sqrt(color(blue)(x)) + x^2sqrt(color(blue)(x))`

We can now factor out the common term giving:

`(x^5 + x^2)sqrt(color(blue)(x))`

If necessary, we can also factor out a common term from the two terms within the parenthesis:

`(x^3x^2 + 1x^2)sqrt(color(blue)(x))`

`(x^3 + 1)x^2sqrt(color(blue)(x))`

Answer 2

I think the correct version is

`sqrt(x^11)+sqrt(x^5)`

`sqrt((x^5)^2*x)+sqrt((x^2)^2*x)`

`|x^5|*sqrtx+x^2*sqrtx`

`x^4*|x|*sqrtx+x^2*sqrtx`

`x^2*sqrtx*(x^2*|x|+1)`

where || =absolute value