Question

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!

Answer 1

`sqrt(192) = 8sqrt(3)`

Explanation:

Your answer is correct. Here's why...

If `a, b >= 0` then:

`sqrt(ab) = sqrt(a)sqrt(b)`

If `a >= 0` then:

`sqrt(a^2) = a`

Find the prime factorisation of `192` and identify square factors:

`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)`