Algebra Examples

$\frac{\sqrt{27 z}}{\sqrt{3 z}}$

Step 1

Combine $\sqrt{27 z}$ and $\sqrt{3 z}$ into a single radical.

$\sqrt{\frac{27 z}{3 z}}$

Step 2

Reduce the expression $\frac{27 z}{3 z}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $27 z$ .

$\sqrt{\frac{3 (9 z)}{3 z}}$

Step 2.2

Factor $3$ out of $3 z$ .

$\sqrt{\frac{3 (9 z)}{3 (z)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (9 z)}{3 z}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{9 z}{z}}$

Step 3

Cancel the common factor of $z$ .

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{9 z}{z}}$

Step 3.2

Divide $9$ by $1$ .

$\sqrt{9}$

Step 4

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

$\sqrt{3^{2}}$

Step 5

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

$3$