How do you simplify $sqrt(12/75)$ ?

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Answer 1 · 2018-06-10T23:58:09

$2/5$

We can leverage the radical property

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

All this is saying is that the square root of the quotient is the same as the quotient of the square roots. We can now rewrite our expression as

$color(blue)(sqrt12)/color(purple)(sqrt75)$

This is equivalent to

$color(blue)((sqrt4*sqrt3))/color(purple)((sqrt25*sqrt3))$

Since we have a $sqrt3$ on the top and bottom, these cancel:

$(sqrt4*cancel(sqrt3))/(sqrt25*cancel(sqrt3))$

And we're left with

$sqrt4/sqrt25$

Which simplifies to

$2/5$

Hope this helps!

How do you simplify sqrt(12/75)sqrt(12/75)?