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

Mar 26, 2018

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

#### Explanation:

$\frac{\sqrt{2}}{\sqrt{5 a b}}$

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

$\left[\frac{\sqrt{2}}{\sqrt{5} \sqrt{a b}}\right] \cdot \left[\frac{\sqrt{5} \sqrt{a b}}{\sqrt{5} \sqrt{a b}}\right]$

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

$\Rightarrow \frac{\sqrt{10} \sqrt{a b}}{5 a b}$

Hence,

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

Hope it helps.