Why don't you tell us what you think the answer to each of this is.
As it is, it appears as if you are asking us to take a test for you.
If you would read underneath it i asked for an explanation plato, you would see i asked if someone could EXPLAIN to me these type of problems and what made the principal of the equation different then the others, you must have skipped that part (and this is not even the whole test). Anyways thanx qbkr, but could you provide an explanation to the steps of solving?
the rules we use are as follows.
let "xroot" represent any root.
in general, by the laws of surds (and exponents):
xroot(a*b) = xroot(x)*xroot(b)
so we can find the product of numbers under the root, and then split them into the roots of the products. usually you do this in such a way, that most of the roots end up as "nice numbers"
e.g. the first question:
sqrt(8a^2) = sqrt(2*4*a^2) = sqrt(2)*sqrt(4)*sqrt(a^2) = sqrt(2)*2a
also, these posts may help:
there are a lot more around, but i can't find them at the moment and i also don't have much time to explain your problems to you. i'm leaving very soon
sqrt(4) is nice since it equals 2 a whole rational number.
sqrt(64) is nice since it is 8
sqrt(36) is nice since it is 6
so for instance:
sqrt(72) that's not nice. but i can change this into sqrt(2*36) = sqrt(2)*sqrt(36)
now sqrt(36) is "nice", so i end up with 6*sqrt(2)
i explain there (in very basic terms) how to go from radicals to exponents.
basically for the sqrt, it is the same as saying to the 1/2 power. and when we raise a number to a power, we multiply the power of the number by the power we are raising it to, and that becomes the new power
so, for example, sqrt(x^2) = (x^2)^(1/2) = x^(1/2 * 2) = x^1 = x
and sqrt(x^3) = (x^3)^(1/2) = x^(3 * 1/2) = x^(3/2)