Question

How do you simplify `(9sqrt25)/sqrt50`?

Answer 1

`9/sqrt2`

Explanation:

`(9 sqrt25)/sqrt50`

`= (9xx5)/sqrt 50`

`sqrt50` can be simplified to `sqrt(25xx2) = 5sqrt 2`

`45 /( 5 sqrt 2)`

= `9 /sqrt2`

Answer 2

`[9sqrt2]/2`

Explanation:

`9sqrt25` = `9 xx 5` = 45

`sqrt50=sqrt25xx2=5sqrt2`

so `[9sqrt25]/sqrt50=45/[5sqrt2]`

dividing by top and bottom by 5 leaves

`9/sqrt2`

If we multiply top and bottom by `sqrt2` this will rationalise it (remove the surd from the denominator)

`9/sqrt2 xx sqrt2/sqrt2` =`[9sqrt2]/2`

Answer 3

`(9sqrt25)/sqrt50 = (9sqrt2)/2`

Explanation:

`sqrt(ab) = sqrta *sqrtb`

So, `(9sqrt25)/sqrt50 =(9sqrt25)/(sqrt25*sqrt2 )=9/sqrt2`

`9/sqrt2 xx sqrt2/sqrt2 = (9sqrt2)/2`