Answer:
The simplest form of [tex]\sqrt{\dfrac{48}{192}}[/tex] is [tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given: [tex]\sqrt{\dfrac{48}{192}}[/tex]
We need to simplify the square root
First we factor numerator and denominator and then cancel the like term from top and bottom.
Factor of 48
[tex]48\rightarrow 2^4\cdot3[/tex]
[tex]192\rightarrow 2^6\cdot3[/tex]
[tex]\Rightarrow \sqrt{\dfrac{2^4\cdot 3}{2^6\cdot 3}}[/tex]
[tex]\Rightarrow \sqrt{\dfrac{1}{2^2}}[/tex]
[tex]\Rightarrow \dfrac{1}{2}[/tex]
Hence, The simplest form of [tex]\sqrt{\dfrac{48}{192}}[/tex] is [tex]\dfrac{1}{2}[/tex]
