How do you simplify #-3\sqrt { 80} + \sqrt { 45}#?

Question

1209 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-15T19:30:01

See a solution process below:

We can rewrite the terms within the radicals as:

#-3sqrt(16 * 5) + sqrt(9 * 5)#

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

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

#-3sqrt(color(red)(16) * color(blue)(5)) + sqrt(color(red)(9) * color(blue)(5)) =>#

#(-3sqrt(color(red)(16))sqrt(color(blue)(5))) + (sqrt(color(red)(9))sqrt(color(blue)(5))) =>#

#(-3 * 4sqrt(color(blue)(5))) + 3sqrt(color(blue)(5)) =>#

#-12sqrt(5) + 3sqrt(5)#

We can now combine the like terms:

#(-12 + 3)sqrt(5) =>#

#-9sqrt(5)#

Answer 2 · 2017-07-15T19:33:44

#-9sqrt5#

#-3sqrt80+sqrt45#

Since #80=16*5#, we can rewrite #sqrt80# as #sqrt16 * sqrt5#. Similarly, we can rewrite #sqrt45# as #sqrt9 * sqrt5#.

#=-3(sqrt16*sqrt5)+(sqrt9 * sqrt5)#

#=-3(4sqrt5)+(3sqrt5)# #->#evaluate radicals

#=-12sqrt5+3sqrt5# #->#multiply #-3# with #4sqrt 5#

#=-9sqrt5# #->#add radicals