Solving the sq. root of 2a^2 (in context of finding distance from (a,a) to origin)?

AnnieMehta

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So the math problem I have for homework (among others) is inherently a geometry problem, but there’s one part I don’t understand:
Using the distance formula, I need to calculate the distance from (a, a), where a>0, to the origin, (0,0).
I end up with something like this:
d= a^2 + a^2.
I didn’t really want to just google the answer and get it done because that’s gonna cause more problems for me, but at this point I really didn’t know how to do it.
I saw that the result ended up being 2a, according to other people on the internet. How would I go about solving a^2 + a^2, and is the answer 2a?

Thanks!!
 
So the math problem I have for homework (among others) is inherently a geometry problem, but there’s one part I don’t understand:
Using the distance formula, I need to calculate the distance from (a, a), where a>0, to the origin, (0,0).
I end up with something like this:
d= (a^2 + a^2).
I didn’t really want to just google the answer and get it done because that’s gonna cause more problems for me, but at this point I really didn’t know how to do it.
I saw that the result ended up being 2a, according to other people on the internet. How would I go about solving a^2 + a^2, and is the answer 2a?

Thanks!!

d= √(a^2 + a^2) = √(2 * a^2) = √(2) * √(a^2) = √(2) * a
 
I often make mistakes solving the square root equations. I don't know why am I so inattentive and what can I do to get rid of this.:rolleyes:
 
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I often make mistakes solving the square root equations. I don't know why am I so inattentive and what can I do to get rid of this.:rolleyes:
There are just a few rules for sqrts so just learn them well. Then when you have a sqrt problem just go over each rule in your head and use the one that applies to the problem you are working on.
 
… I don't know why am I so inattentive and
what can I do to get rid of this …
More practice. ;) That is, maybe you're not so much inattentive as not yet exposed to the patterns enough for your brain to link and encode them (your brain will recognize contradictions, as you work, once you have sufficient experience). We all have variations in our brain network, so some people naturally need more experiences with specific situations than others.

I also think it could help to have a listing of the Properties of Radicals handy, when working with these types of expressions. Pondering the properties might help jog your brain into giving you ideas.

Things get better, with practice. You'll know, when you feel confident -- keep practicing 'till you get there. :cool:

I use this property of radicals a lot, reading it forwards and backwards:

\(\displaystyle \sqrt{m \cdot n} = \sqrt{m} \cdot \sqrt{n}\)
 
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