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

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

Step 1

Combine $\sqrt{a^{3}}$ and $\sqrt{a}$ into a single radical.

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

Step 2

Reduce the expression by cancelling the common factors.

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

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

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

Raise $a$ to the power of $1$ .

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

Factor $a$ out of $a^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $a^{2}$ by $1$ .

$\sqrt{a^{2}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$a$