Question

Rewrite the following in simplified radical form.

√27w^10

Assume that all variables represent positive real numbers.

Answer 1

IS THIS sqrt(27w^2)

Answer 2

yes

Answer 3

wait no, its sqrt(27w^10)

Answer 4

OK
http://www.wolframalpha.com/input/?i=%E2%88%9A27w^10

Answer 5

nice try iv used wolframalpha before, its not simplified radical form

Answer 6

Well, factoring the part under the radical we have:
\[\sqrt{27w^{10}} = \sqrt{(3^2\cdot 3)(w^2\cdot w^2 \cdot w^2\cdot w^2\cdot w^2)}\]

And pulling out each squared factor we get:
\[3\sqrt{3}|w^5|\]

Answer 7

You can also do this the quick way by recalling that \[\sqrt[b]{a^k} = (a)^{k\over b}\]