How do you simplify #sqrt20 + sqrt45#?

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Answer 1 · 2018-03-20T22:12:35

See a solution process below:

First, rewrite the term under each radical as:

#sqrt(4 * 5) + sqrt(9 * 5)#

Now, use this rule for radicals to simplify each radical:

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

#sqrt(color(red)(4) * color(blue)(5)) + sqrt(color(red)(9) * color(blue)(5)) =>#

#sqrt(color(red)(4))sqrt(color(blue)(5)) + sqrt(color(red)(9))sqrt(color(blue)(5)) =>#

#color(red)(2)sqrt(color(blue)(5)) + color(red)(3)sqrt(color(blue)(5))#

Now, factor out the common term to complete the simplification:

#(color(red)(2) + color(red)(3))sqrt(color(blue)(5)) =>#

#color(red)(5)sqrt(color(blue)(5))#