What is #sqrt192# in simplest radical form? Thanks!
I need help checking my extra work for practice and wanted to know how to do #sqrt192# as well as the simplest answer in radical form. The answer I got was #8sqrt3# if this is not the correct answer, please let me know why. If it is, let me know that I am correct so I don't have to worry about failing my math test in a couple of weeks. Thanks!
I need help checking my extra work for practice and wanted to know how to do
1 Answer
Oct 18, 2016
Explanation:
Your answer is correct. Here's why...
If
#sqrt(ab) = sqrt(a)sqrt(b)#
If
#sqrt(a^2) = a#
Find the prime factorisation of
#192 = 2*2*2*2*2*2*3 = 2^6*3 = (2^3)^2*3 = 8^2*3#
So:
#sqrt(192) = sqrt(8^2*3) = sqrt(8^2)*sqrt(3) = 8sqrt(3)#