How do you simplify $sqrt(xyz)*sqrt(2y^3z^4)$ ?

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Answer 1 · 2017-10-02T21:48:45

$y^2z^2sqrt(2xz)$

$sqrt(xyz)* sqrt(2y^3z^4)=> sqrt(2xy^4z^5)$

we can see this as:

$sqrt(2 xx x xx y^4 xx z^4xxz$

We can now extract any exact roots:

The $sqrt(y^4) = y^2$ since $y^2 xx y^2 = y^(2+2)= y^4$

$y^2sqrt(2xx x xx z^4 xx z)$

Do the same for $z^4$ :

$y^2z^2sqrt(2 xx x xx z)$

This is as far as we can go, so:

$y^2z^2sqrt(2xz)$

How do you simplify sqrt(xyz)*sqrt(2y^3z^4)sqrt(xyz)*sqrt(2y^3z^4)?