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.