thank you, Scott or whomever
simplify the square root if 108
ok.
I got 9x12
which then prime factorization = 2.2.3.3.3
then
i get it means the square root of 2.2.3.3.3
but then i get stuck
thank you
well you already have
sqrt( 2^2 * 3^2 * 3 )
= 2*3 * sqrt 3
= 6 sqrt 3
I still don't get the end part
well
sqrt (2^2) = sqrt 4 = 2
sqrt (3^2) = sqrt 9 = 3
sqrt 3 = sqrt 3
in general
sqrt (a^2 b^2) = a b
remember sqrt 36 = 6
sqrt ( 6*6 ) = 6
sqrt (6^2) = 6
all the same written differently
You're welcome! Let's continue simplifying the square root of 108.
You correctly expressed 108 as the product of its prime factors: 2 x 2 x 3 x 3 x 3.
To simplify the square root of 108, we can take out pairs of the same prime factors and leave only one outside the square root. In this case, we have two pairs of 2's and one pair of 3's.
Let's simplify it step by step:
1. Take out one pair of 2's: √(2 x 2 x 3 x 3 x 3) = 2 x √(3 x 3 x 3)
2. Take out one pair of 3's: 2 x √(3 x 3 x 3) = 2 x 3 x √3 = 6√3
Therefore, the simplified square root of 108 is 6√3.
I hope that helps! Let me know if you have any further questions.