Math Problem...PLEASE HELP ME!!!!!, (Algebra 2)?

Question

I have the answer...i just need to know how to get the answer...i have no clue how!!

Here is the question:

8 over √24x

Here is the answer:

2√6x over 3x

The probelm has to do with applying the rules of exponents and radicals.

PLEASE HELP ME!!!!!

Answer 1

This is basically just simplifying the original term. The basic rule is that you want to make the number inside the radical as small as possible by separating it into different squares, and then you want to make it so the denominator is radical free.

So we start with:
8 / √(24x)

If you look carefully, you can separate the terms inside the radical to simplify it. We know that 24 = 4 * 6, and 4 is just 2 squared, so we can take the sq root of 4 and take it out of the radical, do a little simplyifying, and rewrite it as:

8 / √(24x)
= 8 / √(4*6x)
= 8 / 2√(6x)
= 4 / √(6x)

Now we just need to get the radical out of the denominator. To do this, we simply need to multiply by 1, but in the form of
√(6x) / √(6x). Doing this will keep the overall value the same (anything multiplied by 1 is still the same value) but we will get a different form. Then we just have to simplify it a little more to get the final answer

[4 / √(6x)] * [√(6x) / √(6x)]
= 4√(6x) / 6x
= 2√(6x) / 3x

so your final answer is
2√(6x) / 3x

Answer 2

8 over √24x when simplified equals
=2 * 2 * 2 over √4 * √2 * √3X
=2 * 2 * 2 over 2 * √2 * √3X (Because √4 = 2)
=2 * 2 over √2 * √3X (2 from top & bottom gets eliminated)
=√2 * √2 * 2 over √2 * √3X
=√2 * 2 over √3 * X (√2 from top & bottom gets eliminated)
= √3X * √2 * 2 over √3X * √3X (multiply top & bottom by √3X)
= 2√6X over 3X

Answer 3

8/√24x=8/√4*6x
=8/2√6x
=4/√6x
=4/√6x * (√6x/√6x)
=4√6x over 6x
=2√6x over 3x

i hope u understand sumthing!

Answer 4

8/√24x

Multiply numerator and denominator by √24x

(8√24x)/(√24x√24x)

(8√24x)/(24x)

Factor out 4 out numerator radical, 4 becomes 2 because you take the square root.

((8)(2)√6x)/(24x)

(16√6x)/(24x)

Divide both numerator and denominator by 8

(2√6x)/(3x)
.

Answer 5

me neither! sori dude!