Question

How do you simplify `sqrt(2/3)*sqrt(3/7)`?

Answer 1

See a solution process below:

Explanation:

We can use this rule for multiplying radicals:

`sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))`

`sqrt(color(red)(2/3)) * sqrt(color(blue)(3/7)) => sqrt(color(red)(2/3) * color(blue)(3/7)) => sqrt(color(red)(2/color(black)(cancel(color(red)(3)))) * color(blue)(color(black)(cancel(color(blue)(3)))/7)) =>`

`sqrt(2/7)`

If necessary we can rationalize the denominator. Or in other words, remove the radical from the denominator:

We can rewrite the radical as:

`sqrt(2)/sqrt(7) => sqrt(7)/sqrt(7) xx sqrt(2)/sqrt(7) => (sqrt(7) xx sqrt(2))/(sqrt(7))^2 => sqrt(7 xx 2)/7 =>`

`sqrt(14)/7`