How do you simplify the expression #5 sqrt(x^2)#?

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Answer 1 · 2017-03-07T23:17:43

#5sqrt(x^2) = 5x# See a solution process below using rules of radicals and exponents:

First, use this rule of radicals to rewrite this expression:

#root(color(red)(n))(x) = x^(1/color(red)(n))#

#5sqrt(x^2) = 5root(color(red)(2))(x^2) = 5(x^2)^(1/color(red)(2))#

Next, use this rule of exponents to further simplify:

#5(x^color(red)(2))^color(blue)(1/2) = 5x^(color(red)(2) xx color(blue)(1/2)) = 5x^1#

Now, we can complete the simplification using this rule of exponents:

#a^color(red)(1) = a#

#5x^color(red)(1) = 5x#