dividing radicals....need some help please!!!! Oh yeah, and Thank you!!!?

Question

Please help with as much as you can.

1. √6x/√24

2. √45x^2/√9

3. √14x/18x

4. √75xy^7/12xy

5. √2x/9x

Answer 1

1. √6x/√24
=√6x / √6√4
=x/2

2. √45x^2/√9
=√9√5 x^2 /√9
=√5x^2

3. √14x/18x
√14/18

4.√75xy^7/12xy
=5√3xy^7/ 12xy
=5√3y^6 / 12

5. √2x/9x
√2/9

Answer 2

Things to remember
(a)Do not keep radical in the denominator
(b) x^m / x^n = x^m-n

1. √6x/√24
= √6x/√4√6
= x/4

2. √45x^2/√9
= √5√9x^2/√9
= √5x^2

3. √14x/18x
= √14/18

4. √75xy^7/12xy
= √75y^6/12

Answer 3

1) A division of two radicals (of same degree) is the same as the radical of the division.
√6x/√24 = √(6x/24) = √(x/4) = √x / √4 = √x / 2

2) a radical of a multiplication is the same as a multiplication of radicals.
AND
a radical and a power (same degree) cancel out
√45x^2 = √45 * √x^2 = √(5*9) * √x^2
=√5 * √3^2 * √(x^2) = √5 * 3 * x = 3x*√5

For the other ones, we do not know how far the radical extends (use brackets)
e.g., number 5 is
√2* x/9x
√(2x) / 9x
√(2x/9)*x
√(2x/9x)
?

Answer 4

Well, remember you can never have a radical in the denominator (bottom). So for example, in number 5. you are going to have to times the numerator by the radical 9x so that you will be able to cancel the denominator radical. That will leave you with the radical of 81x^2 which really is 9x (with no radical.

Then on the top you are left with the radical of 18x^2. That simplifies to 3x sqare root of 2 all over 9x. Then subtract the "x" 's leaving the bigger number on botoom and simplify. Final answer is 1sqaureroot of 2 all over 3x.

Are you familiar with the rules of dividing squareroots and such?

I can try and help you with that if the help is needed!

Answer 5

1. sqrt(6)x/sqrt24
=sqrt(6)x/2sqrt(6)
=x/2
2. sqrt(45)x^2/sqrt9
=3sqrt(5)x^2/3
=x^2sqrt5
3.sqrt(14)x/18x
sqrt(14)/18
4.xy^7sqrt75/12xy
=5xy^7 sqrt3/12xy
=5y^6sqrt3/12
5.x sqrt2/9x
=sqrt2/9

Answer 6

what is the object? If you are trying to put in the simplest terms, just factor the radicals:

ex: in the first problem,
sqrt(6*x)/sqrt(24) = sqrt(6*x)/sqrt(6*4) = sqrt(6)*sqrt(x)/sqrt(6)*sqrt(4) = sqrt(x)/sqrt(4) = sqrt(x)/2