How do you simplify #sqrt1152-sqrt338#?

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Answer 1 · 2018-05-24T11:56:00

See a solution process below:

First, rewrite the term under each radical as:

#sqrt(576 * 2) - sqrt(169 * 2)#

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

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

#sqrt(color(red)(576) * color(blue)(2)) - sqrt(color(red)(169) * color(blue)(2)) =>#

#sqrt(color(red)(576))sqrt(color(blue)(2)) - sqrt(color(red)(169))sqrt(color(blue)(2)) =>#

#24sqrt(color(blue)(2)) - 13sqrt(color(blue)(2))#

We can now factor out the common term giving:

#(24 - 13)sqrt(color(blue)(2)) =>#

#11sqrt(color(blue)(2))#