Basic algebra concept is puzzling me

[TheKracken]

basic algebra concept is puzzling me...

Homework Statement

I don't understand why √10-5 + √5 = 2√5
Could someone please explain this to me real quick...totally forgot why this is :P

Homework Equations

none

The Attempt at a Solution

here I am! thoughts about it and I am still puzzled does it have anything to do with the fact that √10-5 =√5 and then we add another √5 to it and there is some rule that says that you take one of them away and just put a 2 infront of √5 and it is equivilant?

 

[Dick]

Yes. sqrt(5)+sqrt(5)=2*sqrt(5). Is that really something you forget? It's kind of the definition of multiplication.

 

[TheKracken]

its probably just all the √ and stuff...it often scares me and I think automaticaly different rules apply or something...

could someone explain limit equations with trig functions in them? I have no idea how to figure these out...for example:
limit as x->0 for x/sin3x

 

[Dick]

its probably just all the √ and stuff...it often scares me and I think automaticaly different rules apply or something...

could someone explain limit equations with trig functions in them? I have no idea how to figure these out...for example:
limit as x->0 for x/sin3x

No, no different rules apply. For the second one, do you know limit as u->0 u/sin(u)=1? If so, put u=3x.

 

[TheKracken]

No, no different rules apply. For the second one, do you know limit as u->0 u/sin(u)=1? If so, put u=3x.

so the answer would be 1/3 yes?
now if it was instead sin 5x would it now be 1/5?
thank you for help!

 

[checkitagain]

I don't understand why √10-5 + √5 = 2√5

...does it have anything to do with the fact that √10-5 =√5

TheKracken,

you must use grouping symbols around this radicand, otherwise what
you have is

√(10) - 5 + √5 = 2√5, which is not what you meant.

 

[Dick]

so the answer would be 1/3 yes?
now if it was instead sin 5x would it now be 1/5?
thank you for help!

You're welcome. Sure. The answer is 1/3.