Simplify square root of (162a)/(6a^3)

$\sqrt{\frac{162 a}{6 a^{3}}}$

Step 1

Reduce the expression $\frac{162 a}{6 a^{3}}$ by cancelling the common factors.

Factor $6$ out of $162 a$ .

$\sqrt{\frac{6 (27 a)}{6 a^{3}}}$

Factor $6$ out of $6 a^{3}$ .

$\sqrt{\frac{6 (27 a)}{6 (a^{3})}}$

Cancel the common factor.

$\sqrt{\frac{6 (27 a)}{6 a^{3}}}$

Rewrite the expression.

$\sqrt{\frac{27 a}{a^{3}}}$

Step 2

Cancel the common factor of $a$ and $a^{3}$ .

Factor $a$ out of $27 a$ .

$\sqrt{\frac{a \cdot 27}{a^{3}}}$

Cancel the common factors.

Factor $a$ out of $a^{3}$ .

$\sqrt{\frac{a \cdot 27}{a \cdot a^{2}}}$

Cancel the common factor.

$\sqrt{\frac{a \cdot 27}{a \cdot a^{2}}}$

Rewrite the expression.

$\sqrt{\frac{27}{a^{2}}}$

Step 3

Rewrite $\frac{27}{a^{2}}$ as ${(\frac{3}{a})}^{2} \cdot 3$ .

Factor the perfect power $3^{2}$ out of $27$ .

$\sqrt{\frac{3^{2} \cdot 3}{a^{2}}}$

Factor the perfect power $a^{2}$ out of $a^{2}$ .

$\sqrt{\frac{3^{2} \cdot 3}{a^{2} \cdot 1}}$

Rearrange the fraction $\frac{3^{2} \cdot 3}{a^{2} \cdot 1}$ .

$\sqrt{{(\frac{3}{a})}^{2} \cdot 3}$

Step 4

Pull terms out from under the radical.

$\frac{3}{a} \sqrt{3}$

Step 5

Combine $\frac{3}{a}$ and $\sqrt{3}$ .

$\frac{3 \sqrt{3}}{a}$