Simplify 1/( square root of 28z)

$\frac{1}{\sqrt{28 z}}$

Step 1

Simplify the denominator.

Rewrite $28 z$ as $2^{2} \cdot (7 z)$ .

Factor $4$ out of $28$ .

$\frac{1}{\sqrt{4 (7) z}}$

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

Multiply $\frac{1}{2 \sqrt{7 z}}$ by $\frac{\sqrt{7 z}}{\sqrt{7 z}}$ .

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

Step 3

Combine and simplify the denominator.

Multiply $\frac{1}{2 \sqrt{7 z}}$ by $\frac{\sqrt{7 z}}{\sqrt{7 z}}$ .

$\frac{\sqrt{7 z}}{2 \sqrt{7 z} \sqrt{7 z}}$

Move $\sqrt{7 z}$ .

$\frac{\sqrt{7 z}}{2 (\sqrt{7 z} \sqrt{7 z})}$

Raise $\sqrt{7 z}$ to the power of $1$ .

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

Raise $\sqrt{7 z}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{7 z}}^{2}$ as $7 z$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 z}$ as ${(7 z)}^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{7 z}}{2 {(7 z)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{7 z}}{2 {(7 z)}^{\frac{2}{2}}}$

Rewrite the expression.

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

Simplify.

$\frac{\sqrt{7 z}}{2 (7 z)}$

Step 4

Multiply $2$ by $7$ .

$\frac{\sqrt{7 z}}{14 z}$

Simplify 1/( square root of 28z)

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