How do you simplify $sqrt(5/7)*sqrt(2/5)$ ?

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Answer 1 · 2015-09-29T11:36:06

$sqrt(14)/7$

Since the two radicals have the same index 2, you can combine them under one radical symbol.

$sqrt(5/7)*sqrt(2/5)$
$=sqrt(cancel5/7*2/cancel5)$
$=sqrt(2/7)$

You can leave it there, or you can continue by rationalizing it. To rationalize it, you have to take out the denominator out of the radical symbol.

$sqrt(2/7)$
$=sqrt(2/7*7/7)$
$=sqrt((2*7)/7^2)$
$=sqrt(2*7)/7$
$color(blue)(=sqrt(14)/7)$

How do you simplify sqrt(5/7)*sqrt(2/5)sqrt(5/7)*sqrt(2/5)?