Simplify square root of 27tu^3

$\sqrt{27 t u^{3}}$

Step 1

Rewrite $27 t u^{3}$ as ${(3 u)}^{2} \cdot (3 t u)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) t u^{3}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 3 t u^{3}}$

Factor out $u^{2}$ .

$\sqrt{3^{2} \cdot 3 t (u^{2} u)}$

Move $t$ .

$\sqrt{3^{2} \cdot 3 u^{2} t u}$

Move $3$ .

$\sqrt{3^{2} u^{2} \cdot 3 t u}$

Rewrite $3^{2} u^{2}$ as ${(3 u)}^{2}$ .

$\sqrt{{(3 u)}^{2} \cdot 3 t u}$

Add parentheses.

$\sqrt{{(3 u)}^{2} \cdot 3 (t u)}$

Add parentheses.

$\sqrt{{(3 u)}^{2} \cdot (3 t u)}$

Step 2

Pull terms out from under the radical.

$3 u \sqrt{3 t u}$