is this radical fraction in simplest form?

Question

2 times the square root of 10 over the square root of 12

and

the square root of 32 over the square root of 25

Answer 1

2 times the square root of 10 is fine but 12 can be seperated into radical 4 * 3 and 4 into 2 then the 2s divide themselves out so you get square root of 10 over the square root of 3(some teachers also like real number as a denominator so you may want to times the whole fraction by radical 3 to get radical 30 over 3)
the square root of 32 is 16 *2 so you get 4 * radical 2 and 25 is 5 so you 4 * radical 2 over 5

Answer 2

square root of 12 = square root of (2*2*3) = 2 times square root of 3. You can then simplify the 2's.
10 = 2*5, so this can't be simplify

square root of 32 = square root of (2^5) = 4 times square root of 2
square root of 25 = 5

Answer 3

The first one: no. sqrt(12) = sqrt(4 * 3) = 2 sqrt(3). Plug that in, and you'll see one more simplification.

Now: something you have to consider is whether you're expected to rationalize the denominator. Some people - me among them - think it's just fine to leave radicals in the denominator, but many others don't consider that to be completely simplified. In this case, to rationalize the denominator, you'd multiply the entire fraction by sqrt(3)/sqrt(3). You'll find you're left with no radicals below.

Second: Again, no. What's the square root of 25? And you can write

sqrt(32) = sqrt(16 * 2)

You should be able to take it from there.

Answer 4

The first expression can be simplified to 2 times sq root of 5, all over sq root of 6.

The second is sq root of 16 times sq root of 2, all over sq root of 25. This can be further reduced to 4 times sq root of 2, over 5.