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

2 Answers
May 24, 2018

Answer:

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))#

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