Please help me with this math problem involving radicals!?

Question

http://i37.tinypic.com/32zmgsn.jpg

Click to see.. and could you explain how u did it. thank you!

Answer 1

(18)^2/x^3 > or equal to 0 for this to work in the real number system.

any negative number of x will make x^3 < 0 and hence (18)^2/x^3<0.

Therefore x > 0, it cannot equal 0 as you cannot divide by 0.

Answer 2

:S,what the !@%* is these?

Answer 3

√(18²/z³) ..........

Well, we can obviously take 18/z out that to get (18/z)(√(1/z)) = 18/z√z. You can simplify further what's under the square root sign by being a little tricky.

Note that 1/z = z/z² so √1/z = √(z/z²) = (√z)/z

So now we have (18/z)(√z)/z = 18√z/z²

You can see that 18√z/z² = 18/z^1.5 which of course = 18/z√z

Answer 4

First thing you can do is separate 18^2/(z^3) into 18^2/(z^2) * (1/z)

Pull 18/z out of the radical so you have (18/z)* √(1/z)

Now, you can't leave a fraction under a radical sign, so multiply top and bottom of the fraction by z:

(18/z)*√(1z/z^2)

Pull the (1/z^2) out of the radical:

[18/(z^2)]*√(z)

_/

Answer 5

sqrt[(18^2)/(z^3)]

=sqrt(18^2) / sqrt(z^3)

=18/[zsqrt(z)]