How do you simplify $sqrt(2/3)*sqrt(6/5)$ ?

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Answer 1 · 2018-06-09T18:21:49

$(6sqrt5)/15$

Use the rule for radicals of the same degree:

$sqrta * sqrtb=sqrt(a*b)$

$sqrt(2/3)*sqrt(6/5)=sqrt(2/3*6/5)=sqrt(12/15)$

now use the rule for radicals of the same degree:

$sqrt(a/b) = sqrta/sqrtb$

$sqrt(12/15)=sqrt12/sqrt15$

now rationalize the denominator:

$sqrt12/sqrt15*sqrt15/sqrt15 = sqrt180/15 = (6sqrt5)/15$

Answer 2 · 2018-06-09T18:22:15

$(2*sqrt(5))/5$

We get by
$sqrt(a)*sqrt(b)=sqrt(ab)$ for $a,b>=0$
so we obtain

$sqrt(2/3)*sqrt(6/5)=sqrt(4/5)=2/sqrt(5)=(2*sqrt(5))/5$

How do you simplify sqrt(2/3)*sqrt(6/5)sqrt(2/3)*sqrt(6/5)?