Respuesta :

esriddersi
1. [tex] \sqrt{ \frac{48}{192}} = \frac{ \sqrt{48} }{\sqrt{192}} [/tex]
2. [tex] \sqrt{48} = 4 \sqrt{3}; \sqrt{192} = 8\sqrt{3} [/tex]
3. [tex] \frac{4\sqrt{3}}{8 \sqrt{3}} = \frac{4}{8} = \frac{1}{2} \text{ --- Answer} [/tex]

Hope this helps! :D
isyllus

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]

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