Question

How do you simplify `sqrt45/(4sqrt81)`?

Answer 1

`sqrt(5)/12`

Explanation:

`1`. Start by multiplying the numerator and denominator by `sqrt(81)/sqrt(81)` to get rid of the radical in the denominator. Note that the value of the fraction would not change since `sqrt(81)/sqrt(81)=1`.

`sqrt(45)/(4sqrt(81))`

`=sqrt(45)/(4sqrt(81))(sqrt(81)/sqrt(81))`

`2`. Simplify.

`=sqrt(45*81)/(4(sqrt(81)sqrt(81)))`

`=sqrt(3645)/(4(81))`

`=sqrt(3645)/324`

`3`. Using a perfect square, break down the radical in the numerator.

`=sqrt(27^2*5)/324`

`4`. Simplify.

`=(27sqrt(5))/324`

`=(color(red)cancelcolor(black)27^1sqrt(5))/color(red)cancelcolor(black)324^12`

`=color(green)(|bar(ul(color(white)(a/a)sqrt(5)/12color(white)(a/a)|)))`