Question

Simplify √16n/m^3 1. 4√mn/n^2 2.4√mn/m 3.√mn/4m 4. 4√mn/m^2

Answer 1

Answer:
`4.\ \ \ (4√(mn))/(m^2)` .

Explanation:

The given expression:
`\sqrt{(16n)/(m^3)}`

'

since
`16=4^2`

`m^3=m^(2+1)= m^2* m` [
`a^(n+m)=a^n* a^m`]

Now, the given expression becomes,

`\sqrt{(4^2n)/(m^2*n)}=(4√(n))/(m√(m))`

Since there is root in denominator , so we need to rationalize

`(4√(n))/(m√(m))*(√(m))/(√(m))=(4√(mn))/(m*√(m)*√(m) )\\\\=(4√(mn))/(m* m)\\\\=(4√(mn))/(m^2)`

Hence, the correct option is
`4.\ \ \ (4√(mn))/(m^2)` .