Question

What is the simplified form of square root of 48/192 ?

Answer 1

1.
`\sqrt{ (48)/(192)} = ( √(48) )/(√(192))`
2.
`√(48) = 4 √(3); √(192) = 8√(3)`
3.
`(4√(3))/(8 √(3)) = (4)/(8) = (1)/(2) \text{ --- Answer}`

Hope this helps! :D

Answer 2

The simplest form of
`\sqrt{(48)/(192)}` is
`(1)/(2)`

Explanation:

Given:
`\sqrt{(48)/(192)}`

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

`48\rightarrow 2^4\cdot3`

`192\rightarrow 2^6\cdot3`

`\Rightarrow \sqrt{(2^4\cdot 3)/(2^6\cdot 3)}`

`\Rightarrow \sqrt{(1)/(2^2)}`

`\Rightarrow (1)/(2)`

Hence, The simplest form of
`\sqrt{(48)/(192)}` is
`(1)/(2)`