Question

What is `sqrt(1/90)`?

Answer 1

`(sqrt 1)/(sqrt90)=(sqrt 10)/(30)`

Explanation:

Simplify.

`(sqrt 1)/(sqrt90)`

Simplify `sqrt 1` to `1`.

`1/(sqrt90)`

Factor `sqrt 90`.

`1/(sqrt (3xx3xx2xx5))`

Simplify.

`1/(sqrt(3^2xx2xx5))`

Apply square root rule `sqrt( a^2)=a`.

`1/(3sqrt(2xx5))`

Simplify.

`1/(3sqrt 10)`

Rationalize the denominator.

`1/(3sqrt 10)xx(sqrt10)/(sqrt 10)`

`(sqrt 10)/(3sqrt 10sqrt 10)`

Apply square root rule `sqrtasqrta=a`.

`(sqrt 10)/(3xx10)`

Simplify.

`(sqrt 10)/(30)`