Question

3√12•√6

please show a step by step explanation ​

Answer 1

Answer:
`18√(2)\\\\`

This is the same as saying 18*sqrt(2) or you could say 18√2

============================================================

Step-by-step explanation:

We'll be using this square root rule:
`√(A)*√(B) = √(A*B)`

So we could have this as our steps:

`3√(12)*√(6)\\\\3√(12*6) \ \text{ ... Apply the rule mentioned}\\\\3√(72)\\\\3√(36*2)\\\\3√(36)*√(2) \ \text{ ... Apply the rule again, but in reverse}\\\\3*6*√(2)\\\\18√(2)\\\\`

Therefore,
`3√(12)*√(6) = 18√(2)`

The basic idea is to first combine the roots using that rule. From there, we factor the radicand such that we pull out the largest perfect square factor. This will allow us to break the root apart and fully simplify it.