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# Algebra

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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

(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.