What is the cube root of 297?

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Answer 1 · 2015-09-21T23:14:26

#root(3)(297) = 3root(3)(11)#

#root(3)(297)#

Factor it out, sice #2+9+7 = 18# we know 297 is divisible by 9.

#root(3)(297) = root(3)(33*9)#

Since #3+3 = 6# we know 33 is divisible by 3

#root(3)(33*9) = root(3)(11*3*9)#

11 is a prime number so there's no more factoring do. We know that #9 = 3^2#, so we can rewrite #3*9 = 3*3^2 = 3^3#

#root(3)(33*9) = root(3)(11*3^3)#

The #3^3# can go out of the root, so

#root(3)(297) = 3root(3)(11)#