Simplify by combining like terms. 9v5 -v80

Question

Simplify by combining like terms.  9√5 -√80

Can I please get some help on this? Thank you!

 

Answer 1

Hi, Abby!

 

When simplifying math expressions that have radical symbols in them (like square roots), "like terms" are terms that have the same radicand (number under the radical symbol).  With that in mind, these directions are instructing you to rewrite √80 in such a way that it has a √5 part, if possible, and then combine like terms.

 

To rewrite √80:  We can break √80 into any grouping of radicals that multiply together to get to 80.  For instance, √80 can be rewritten as √8*√10.  Since our goal is to have our rewritten version include a √5, let's rewrite √80 as √16*√5.

 

9√5 - √80 = 9√5 - √16*√5 = 9√5 - 4√5 = (9 - 4)*√5 = 5√5

 

I hope that this is helpful!

 

Patty