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When sqrt(112) is simplified, the result is a*sqrt(b), where a is an integer, and b is a positive integer. If b is as small as possible, then what is a + b?

 Dec 19, 2021
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To simplify radicals such as these, there are multiple methods. One method is to find the prime factorization of the number and edit it from there.

(2*2*2*2*7) is the prime factorization for 112. You can pull out pairs of numbers to the front of the sqrt, although cancel one in the process. this would then be \(2*2\sqrt7\) this is then simplified to \(4\sqrt7\), which is the answer.

 Dec 19, 2021

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