Can someone explain to me how to solve these questions. And what they mean by find the principal square root or how its different then finding a regular square root. All help is appreciated. Thanx

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- May 16th 2007, 11:45 AM #1

- May 16th 2007, 03:34 PM #2

- May 16th 2007, 04:00 PM #3
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?

- May 16th 2007, 04:06 PM #4
do you know how to go from radicals to powers? if so, this will be a lot easier to understand.

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:

http://www.mathhelpforum.com/math-he...some-help.html

http://www.mathhelpforum.com/math-he...tial-form.html

http://www.mathhelpforum.com/math-he...root-help.html

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

- May 16th 2007, 04:12 PM #5

- May 16th 2007, 04:15 PM #6
here i say "nice numbers" to mean that their roots are whole rational numbers that we know the various roots of.

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)

- May 16th 2007, 04:17 PM #7

- May 16th 2007, 04:19 PM #8

- May 16th 2007, 04:20 PM #9

- May 16th 2007, 04:22 PM #10

- May 16th 2007, 04:24 PM #11

- May 16th 2007, 04:29 PM #12

- May 16th 2007, 04:33 PM #13
see http://www.mathhelpforum.com/math-he...tial-form.html

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)

- May 16th 2007, 04:38 PM #14

- May 16th 2007, 04:48 PM #15