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

1 Answer
smendyka
Aug 23, 2017

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#

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