Answer:
[tex]\displaystyle \frac{\sqrt{2}}{x^2}[/tex]
Step-by-step explanation:
Dividing Radicals
Given the division of radicals:
[tex]\displaystyle \frac{\sqrt{Z}}{\sqrt{Y}}[/tex]
We can join both arguments of the radicals into one simple radical as follows:
[tex]\displaystyle \sqrt{\frac{Z}{Y}}[/tex]
We are given the expression:
[tex]\displaystyle 2\frac{\sqrt{24}}{\sqrt{48x^4}}[/tex]
Joining them in a single radical:
[tex]\displaystyle 2\frac{\sqrt{24}}{\sqrt{48x^4}}=2\sqrt{\frac{24}{48x^4}}[/tex]
Simplifying the fraction:
[tex]\displaystyle 2\sqrt{\frac{24}{48x^4}}=2\sqrt{\frac{1}{2x^4}}[/tex]
Multiplying by 2 in numerator and denominator:
[tex]\displaystyle 2\sqrt{\frac{1}{2x^4}}=2\sqrt{\frac{2}{4x^4}}[/tex]
The denominator is a perfect square:
[tex]\displaystyle 2\sqrt{\frac{2}{4x^4}}=2\frac{\sqrt{2}}{2x^2}[/tex]
Simplifying by 2:
[tex]\boxed{\displaystyle \frac{\sqrt{2}}{x^2}}[/tex]
