Simplify by factoring. Type the exact answer, using radicals as needed.
\(\sqrt{120p^{17}}\)
Answer (2)
120 ('p' to the 17th power) = (4 x 30) x ('p' to the 16th power) x ('p')
The square root of all that is √4 x √30 x √('p' to the 16th power) x √p
Take the square roots of the ones you know: 2 x √30 x ('p' to the 8th power) x √p
So finally, it's
2 ('p' to the 8th power) √(30 p) .
The simplified form of 120 p 17 is 2 p 8 30 p . This involves factoring out perfect squares and applying the square root property. The final answer combines integers and variables under the square root in a simplified manner.
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