How do you simplify #sqrt(x^11)+sqrt(x^5)#?
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"What intermolecular forces are present in #CO_2#?"
See a solution process below:
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
