How do you evaluate #\sqrt { 12z ^ { 8} }#?

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Answer 1 · 2017-06-27T19:05:07

See a solution process below:

First, rewrite this expression as:

#sqrt(4z^8 * 3)#

Now, use this rule of radicals to simplify the expression:

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

#sqrt(color(red)(4z^8) * color(blue)(3)) = sqrt(color(red)(4z^8)) * sqrt(color(blue)(3)) = 2z^4 * sqrt(3) = 2z^4sqrt(3)#

If necessary:

#sqrt(3) = 1.732# rounded to the nearest thousandth.

Then:

#2z^4sqrt(3) = 2z^4 * 1.732 = 3.464z^4# rounded to the nearest thousandth.