Checking square roots, we see that 142 = 196 and 152 = 225. Our answer is not an integer, so we try simplify it into the product of an integer and a radical.
We do this by listing each product combo of 216 checking for integer square root values below: √216 = √1√216 √216 = √2√108 √216 = √3√72 √216 = √4√54 √216 = √6√36 √216 = √8√27 √216 = √9√24 √216 = √12√18
From that list, the highest factor that has an integer square root is 36. Therefore, we use the product combo √216 = √36√6 Evaluating square roots, we see that √36 = 6
Simplifying our product of radicals, we get our answer: √216 = 6√6
Therefore, we can factor out 6 from the radical, and leave 6 under the radical
We can factor out the following portion using the highest even powers of variables: √ = = Our leftover piece under the radical becomes 6√6v Our final answer is the factored out piece and the expression under the radical 6√6v