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

Question

1929 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-02T23:29:08

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

with restriction $u, v \geq 0$ $u, v >= 0$

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

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

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

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

$= \sqrt{8 u^{8} v^{3} \cdot 2 u^{5} v^{6}}$ $=sqrt(8u^8v^3*2u^5v^6)$

$= \sqrt{16 u^{13} v^{9}}$ $=sqrt(16u^13v^9)$

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

$= 4 u^{6} v^{4} \sqrt{u v}$ $= 4u^6v^4sqrt(uv)$

How do you simplify √8u8v3√2u5v6sqrt(8u^8 v^3) sqrt(2u^5 v^6)?