The square root of 80 p to the 3rd

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√(80 p³ = √ (16 x 5 x p² x p) You know the square roots of 16 and p , so you can take them out of the radical. = (4p) x √(5p)


I added pictures, but I don't know how they'll come out when I post this. Sorry if it ends up looking weird :/ You should start by factoring the number inside the cube root/radical sign, which in this case is 80. If you remember how to do factor trees, just do that with the number 80. The p is already prime, so you don't need to worry about it at first. (see picture 1) Now see if there are any triplets of prime numbers. In this case, there is a triplet of twos (see picture 2), so you bring down one 2 to your answer (see picture 3). If there had been two triplets, you would have brought both numbers down and multiplied them. There should be three prime numbers left: 2, 5, and p. (see picture 4) Go back down to your answer, put a cube root/radical sign next to the 2, and put your prime numbers in the cube root/radical. You should have 2∛2·5p. 2·5 can be simplified to 10, so your final answer will be 2∛10p (see picture 5).

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