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

1 Answer
Jul 2, 2015

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

with restriction u, v >= 0

Explanation:

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)