I'm having some trouble in Algebra 1 with simplifying radicals. Could you make it more clear?

Question

What I don't understand is how to clear a radical when it is a denominator and how to multiply a regular number by a radical.
For example:
the square root of 4 divide it by the square root of 12.
I get that eventually it will be 2 over radical 12. Now you multiply the top and bottom by radical 12 but what I don't get is how you multiply a 2 and a radical 12.....could you explain?

Answer 1

Rule: You CANNOT have a radical in the denominator.
To get rid of one, you rationalize the denominator. Basically, you multiply the invalid fraction by 1 (since number x 1=number). The 1 is the radical in the denominator over itself.

Ex. 12/rad 2

RTD-12/rad 2 * rad 2/rad 2<---this fraction=1
rad 2 in the denominator of the second fraction multiplies with rad 2 in the denominator of the first fraction. Sq root of x times sq root of x is x right? so you get 12 (rad 2)/2. Get it?

Answer 2

sqrt of 12= sqrt 4 x sqrt 3= 2sqrt3
sqrt 4=2

2/2sqrt3 x 2sqrt3/2sqrt3 (you can't have a radical in the denominator and when you multiply a sqrt by a sqrt, the result is a regular number without a radical. So it'd be 2x2=4, sqrt3xsqrt3=3 4x3=12)

4sqrt3/12

Answer 3

"issues interior the container stay interior the container, and issues outdoors the container stay outdoors." 3*(8^a million/2) = 6*(2^a million/2) on condition that 8 could be broken down into 4*2, you are able to take the sqrt of four and placed it outdoors the unconventional. So 3*2=6. then you are left with sqrt of two interior the unconventional. The sqrt of sixteen could be broken down into the sqrt of four * the sqrt of four. So then you are left with 2*2*2. you're left with 6*(sqrt2) + 8. For #2 it simplifies to m/n. The powers cancel with the sqare root. For #3 it simplifies to (sqrt of m * absolute fee of m)