How do you simplify #sqrt72+sqrt50#?

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Answer 1 · 2018-03-03T16:06:01

See a solution process below:

Use this rule for radicals to rewrite both radicals:

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

#sqrt(72) + sqrt(50) =>#

#sqrt(color(red)(36) * color(blue)(2)) + sqrt(color(red)(25) * color(blue)(2)) =>#

#(sqrt(color(red)(36)) * sqrt(color(blue)(2))) + (sqrt(color(red)(25)) * sqrt(color(blue)(2))) =>#

#6sqrt(color(blue)(2)) + 5sqrt(color(blue)(2))#

Now, we can factor our the common term to complete the simplification:

#(6 + 5)sqrt(color(blue)(2))#

#11sqrt(2)#