Question

How do you simplify `sqrt 2/sqrt(5ab)`?

Answer 1

`color(red)(sqrt(2)/sqrt(5ab)=(sqrt(10)sqrt(ab))/(5ab)`

Explanation:

Given the radical expression:

`sqrt(2)/sqrt(5ab)`

This expression can be written as

`sqrt(2)/(sqrt(5)*sqrt(ab)` using the rule

`color(blue)(sqrt(pqr) = sqrt(p)*sqrt(q)*sqrt(r)=sqrt(p)*sqrt(qr)`

Multiply and divide by the conjugate of the denominator

`[sqrt(2)/(sqrt(5)sqrt(ab)]]*[(sqrt(5)sqrt(ab))/(sqrt(5)sqrt(ab)]]`

`rArr [sqrt(2)sqrt(5)sqrt(ab)]/[sqrt(5)sqrt(5)sqrt(ab)sqrt(ab]`

Using the rule, `color(blue)(sqrt(m)*sqrt(m)=m`, simplify

`rArr (sqrt(10)sqrt(ab))/(5ab)`

Hence,

`color(red)(sqrt(2)/sqrt(5ab)=(sqrt(10)sqrt(ab))/(5ab)`

Hope it helps.