Math question

[NOLAdentist2016]

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I was taking a practice test, and I want to figure out if the book is wrong or if I just am doing these kinds of problems wrong. Also, I can't get the square root sign or numbers in here, so i'll just explain in words. The question is:

What is the square root of 500 squared plus 200 squared? (nothing is in parenthesis.)

I assumed I could take out a "500" and a "200", then add together to get 700. that wasn't an answer choice tho. The correct answer made me multiply them out, add them together, than take it all out at once.

 

[jwnichols21]

I was taking a practice test, and I want to figure out if the book is wrong or if I just am doing these kinds of problems wrong. Also, I can't get the square root sign or numbers in here, so i'll just explain in words. The question is:

What is the square root of 300 squared plus 200 squared? (nothing is in parenthesis.)

I assumed I could take out a "300" and a "200", then add together to get 500. that wasn't an answer choice tho. The correct answer made me multiply them out, add them together, than take it all out at once.

Where is this question from?

 

[indigenoustw]

I was taking a practice test, and I want to figure out if the book is wrong or if I just am doing these kinds of problems wrong. Also, I can't get the square root sign or numbers in here, so i'll just explain in words. The question is:

What is the square root of 300 squared plus 200 squared? (nothing is in parenthesis.)

I assumed I could take out a "300" and a "200", then add together to get 500. that wasn't an answer choice tho. The correct answer made me multiply them out, add them together, than take it all out at once.

So your question is...

sqrt(300^2 + 200^2)

Simplest is probably using a calculator. However, there are other ways. For instance...

1.
A simple way would be seeing 300^2 as (3^2)(100^2) and 200^2 as (2^2)(100^2), so you can factor out 100^2 from the two terms, take the squre root = 100, and then the question will become 100*sqrt(9+4) which is 100*sqrt(13).

2.
Hard way..
Remember your (a+b)^2 = a^2 + 2ab + b^2?
You can complete the square by having sqrt(300^2 + 2(300)(200) + 200^2 - 2(300)(200))
So the question becomes sqrt(500^2 - 1200)...
Well it's not any simpler since it's a harder route.

But really, it's not that hard to calculate 300^2 straight and 200^2 straight and add up the numbers.

Good luck on your studies!