Question

How do you simplify `sqrt(350)`?

Answer 1

`5sqrt14`

Explanation:

search for the factors of `350` looking for one that is a perfect square.

In this case `25 xx 14`

`25` being the perfect square.

`sqrt350 = sqrt ( 25 xx 14 )`

now `sqrt(ab) = sqrta xx sqrtb` (so long as at least one of `a` and `b` is not negative)

`rArr sqrt(25 xx 14) = sqrt25 xx sqrt14`

The factors of `14` do not contain any square numbers apart from `1` and so `sqrt14` cannot be simplified any further.

`rArr sqrt350 = 5sqrt14`

Answer 2

`5timessqrt(14)`

Explanation:

`350=35times10=7times5times2times5=2times5^2times7`

`sqrt(350)=sqrt(2times5^2times7)=sqrt(5^2)timessqrt(2times7)=`

`5timessqrt(2times7)=5timessqrt(14)`