Question

How do you simplify `sqrt50/(3sqrt2)`?

Answer 1

`5/3`

Explanation:

`sqrt50/(3sqrt2)=`

`sqrt(25*2)/(3sqrt2)=`

`(5cancelsqrt2)/(3cancelsqrt2)=`

`5/3`

Answer 2

`5/3`

Explanation:

`"using the "color(blue)"law of radicals"`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`rArrsqrt50=sqrt(25xx2)=sqrt25xxsqrt2=5sqrt2`

`rArr(sqrt50)/(3sqrt2)=(5cancel(sqrt2))/(3cancel(sqrt2))=5/3`

Answer 3

`+-5/3`

Explanation:

Let's start by thinking about the number `50`, not `sqrt50`. We know its factors are:

• `25` and `2`
• `10` and `5`

So the factors of `sqrt50` are:

• `color(blue)(sqrt25)` and `color(blue)(sqrt2)`
• `sqrt10` and `sqrt5`

We can use the first set of factors to rewrite our expression as

`color(blue)(sqrt25*cancelsqrt2)/(3cancelsqrt2)`

The `sqrt2` will cancel on the top and bottom, and we're left with

`sqrt25/3`

Which can be simplified to

`+-5/3`

Hope this helps!