How do you simplify $sqrt(8u^8 v^3) sqrt(2u^5 v^6)$ ?

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Answer 1 · 2015-07-02T23:29:08

$sqrt(8u^8v^3)sqrt(2u^5v^6) = 4u^6v^4sqrt(uv)$

with restriction $u, v >= 0$

If $sqrt(8u^8v^3)$ is defined then $8u^8v^3 >= 0$

If $sqrt(2u^5v^6)$ is defined then $2u^5v^6 >= 0$

Use $sqrt(a)sqrt(b) = sqrt(ab)$ when $a, b >= 0$ to get:

$sqrt(8u^8v^3)sqrt(2u^5v^6)$

$=sqrt(8u^8v^3*2u^5v^6)$

$=sqrt(16u^13v^9)$

$=sqrt((4u^6v^4)^2uv)$

$= 4u^6v^4sqrt(uv)$

How do you simplify sqrt(8u^8 v^3) sqrt(2u^5 v^6)sqrt(8u^8 v^3) sqrt(2u^5 v^6)?