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

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Answer 1 · 2018-03-26T13:05:03

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

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.

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