Simplify ( square root of 7^3)/( square root of 7)

$\frac{\sqrt{7^{3}}}{\sqrt{7}}$

Step 1

Combine $\sqrt{7^{3}}$ and $\sqrt{7}$ into a single radical.

$\sqrt{\frac{7^{3}}{7}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{7^{3}}{7}$ by cancelling the common factors.

Factor $7$ out of $7^{3}$ .

$\sqrt{\frac{7 \cdot 7^{2}}{7}}$

Factor $7$ out of $7$ .

$\sqrt{\frac{7 \cdot 7^{2}}{7 (1)}}$

Cancel the common factor.

$\sqrt{\frac{7 \cdot 7^{2}}{7 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{7^{2}}{1}}$

Divide $7^{2}$ by $1$ .

$\sqrt{7^{2}}$

Step 3

Raise $7$ to the power of $2$ .

$\sqrt{49}$

Step 4

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}}$

Step 5

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

$7$