SOLUTION: How do I add sqrt486 plus 2sqrt384? The answer I have was 531,108 For sqrt49 +sqrt 9 I got an answer of 2,482, but I am not sure if this is right either. I understand this whe

Algebra ->  Radicals -> SOLUTION: How do I add sqrt486 plus 2sqrt384? The answer I have was 531,108 For sqrt49 +sqrt 9 I got an answer of 2,482, but I am not sure if this is right either. I understand this whe      Log On


   

Question 241022: How do I add sqrt486 plus 2sqrt384?
The answer I have was 531,108
For sqrt49 +sqrt 9 I got an answer of 2,482, but I am not sure if this is right either.
I understand this when there is an exponent with it but I am not sure about these.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
No, I'm afraid you missed this concept!
The second question is easiest, so let's do it first.
sqrt%2849%29%2Bsqrt%289%29
You have to do the square roots first, and THEN you add the results together, but ONLY IF YOU HAVE LIKE TERMS or LIKE RADICALS!!
7+%2B+3
10 FINAL ANSWER for the second part of your question!

Now, the FIRST part of your question is much harder!! In fact, I don't know how they could have made this problem any harder for you! (If you don't understand my explanation here, PLEASE see the note at the end of this problem telling you about my website which has some MUCH EASIER problems to help you get started on this concept!!)

sqrt%28486%29+%2B+2%2Asqrt%28384%29

The first step is to SIMPLIFY each square root SEPARATELY! You have to try to find a perfect square that is a factor of 486. It just so happens that the PERFECT SQUARE 81 divides evenly into 486. It goes 6 times, so you can write
486=81*6.

Now do the same thing for 384. Find a perfect square that goes evenly into 384. I can't think of a perfect square that goes into this, but the previous part, square root of 486, came out with a leftover factor of 6. Do you think maybe 6 goes into 384? Indeed it does. It goes 64 times, which just happens to be a perfect square!! You can write
384=64*6

(I told you this was a HARD ONE!!)
NOW,

sqrt%28486%29%2B2%2Asqrt%28384%29
sqrt%28____%29%2Asqrt%28____%29+%2B+2%2Asqrt%28____%29%2Asqrt%28____%29+
sqrt%2881%29%2Asqrt%286%29+%2B+2%2Asqrt%2864%29%2Asqrt%286%29+

Now, DO the square roots that you know how to do, and leave the other ones alone!
9%2Asqrt%286%29+%2B+2%2A8%2Asqrt%286%29+
9%2Asqrt%286%29+%2B+16%2Asqrt%286%29+

Now, notice that you have both square roots EXACTLY the same!! This means that you can COMBINE LIKE TERMS! Add the 9 + 16, and you get 25!
25%2Asqrt%286%29

I warned you that this was a HARD problem!! You probably need to see my own website in order to get some EASIER problems before you can really understand this one! I have a LOT of resources on my own website on the topic of SQUARE ROOTS. To find my website, do a "BING" or a "GOOGLE" search for my last name "Rapalje". Near the top of the search list, you should see "Rapalje Homepage." Click on this, and look near the top of my homepage for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 5" for "Section 5.01, Square Roots" and "Section 5.03 Combining Like Radicals." This is my own explanation especially written for students who have trouble understanding math. I wrote this to students, NOT mathematicians, and I think you will find it easier to understand than your own traditional textbooks!! In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR.

In addition, I have a video of me teaching this topic in the classroom a few years ago. To see this FREE video, from my Homepage, look for "Rapalje Videos in Living Color". Select "Basic Algebra", and look for "Radicals (Square Roots)".

If you like my website, please recommend it to family and friends who have trouble understanding math!! It's ALL FREE!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus