Find the square root of [tex]80p^3[/tex].

√(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)

Answered by AL2006 | 2024-06-10

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).

Answered by tommoholic13 | 2024-06-10

The square root of 80 p 3 can be simplified to 4 p 5 p ​ by breaking down the components into factors and applying the square root. We take the square roots of the constant and the variable parts. The simplified form gives an expression that is easier to work with.
;

Answered by AL2006 | 2024-12-24