SOLUTION: simplify: square root of 112 + square root of 28. I don't remember the steps to doing this. Can you help?

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Question 90866: simplify: square root of 112 + square root of 28.
I don't remember the steps to doing this. Can you help?
Found 2 solutions by throwabunny, bucky:
Answer by throwabunny(3) About Me  (Show Source):
You can put this solution on YOUR website!
all you have to do is find the factors and see which ones repeat.
112 = 2x2x2x2x7
28=2x2x7
And under a radical sign, you can take out the ones that repeat twice and put it in front.
So therefore, 112 = 4 square root of 7, and 28 = 2 square root of 7.
Since both have square roots of seven, add them together and you get 6 square root of 7.
hope that helped :)

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
For this problem you use the rule that says:
.
sqrt%28a%2Ab%29+=+sqrt%28a%29%2A+sqrt%28b%29
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Then the trick is to find a value for one of the variables (a or b) that is a perfect
square.
.
Let's start with 112. After playing with factors of 112 for a while you can come up with
the factors 16*7. Notice that 16 is a perfect square. And now you can apply the rule:
.
sqrt%28112%29+=+sqrt%2816%2A7%29+=+sqrt%2816%29%2Asqrt%287%29
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Then you can take the square root of 16 to get 4. So you can replace the square root of
16 by 4 and you have 4%2Asqrt%287%29. So you have simplified sqrt%28112%29 down to
4%2Asqrt%287%29.
.
You can next apply the same sort of simplification to sqrt%2828%29. Notice that 28
can be factored into 4*7 and that 4 is a perfect square. Applying the rule gives:
.
sqrt%2828%29+=+sqrt%284%2A7%29+=+sqrt%284%29%2Asqrt%287%29
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Then find the square root of 4 ... which is 2 and replace sqrt%284%29 by 2 to get:
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sqrt%2828%29+=+sqrt%284%2A7%29+=+sqrt%284%29%2Asqrt%287%29+=+2%2Asqrt%287%29
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So we have simplified the second term of the problem down to 2%2Asqrt%287%29
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Substitute these two into the original problem:
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sqrt%28112%29+%2B+sqrt%2828%29
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becomes
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4%2Asqrt%287%29+%2B+2%2Asqrt%287%29
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Then you can add these two directly to get 6%2Asqrt%287%29. If it helps you to visualize
this step you can factor out sqrt%287%29 from the two terms and get:
.
%284+%2B+2%29%2Asqrt%287%29
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and then just add the two numbers in the parentheses to get 6%2Asqrt%287%29.
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You can quickly verify this on a calculator. The square root of 112 is 10.58300524 and
the square root of 28 is 5.291502622. And if you add these two together (as the original problem
called for) you get 15.87450786.
.
Then take the answer 6%2Asqrt%287%29. Using a calculator you find that sqrt%287%29 is
2.645751311. Multiply that by 6 and you have 15.87450787. Close enough to the other way.
The error in the very last decimal place is caused by the calculator rounding off.
.
Hope this helps you to understand the problem and a method you can use to do it.