Simplify (6w)/( square root of 25w)

$\frac{6 w}{\sqrt{25 w}}$

Step 1

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$\frac{6 w}{\sqrt{5^{2} w}}$

Pull terms out from under the radical.

$\frac{6 w}{5 \sqrt{w}}$

Step 2

Multiply $\frac{6 w}{5 \sqrt{w}}$ by $\frac{\sqrt{w}}{\sqrt{w}}$ .

$\frac{6 w}{5 \sqrt{w}} \cdot \frac{\sqrt{w}}{\sqrt{w}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{6 w}{5 \sqrt{w}}$ by $\frac{\sqrt{w}}{\sqrt{w}}$ .

$\frac{6 w \sqrt{w}}{5 \sqrt{w} \sqrt{w}}$

Move $\sqrt{w}$ .

$\frac{6 w \sqrt{w}}{5 (\sqrt{w} \sqrt{w})}$

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

$\frac{6 w \sqrt{w}}{5 ({\sqrt{w}}^{1} \sqrt{w})}$

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

$\frac{6 w \sqrt{w}}{5 ({\sqrt{w}}^{1} {\sqrt{w}}^{1})}$

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

$\frac{6 w \sqrt{w}}{5 {\sqrt{w}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{6 w \sqrt{w}}{5 {\sqrt{w}}^{2}}$

Rewrite ${\sqrt{w}}^{2}$ as $w$ .

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

$\frac{6 w \sqrt{w}}{5 {(w^{\frac{1}{2}})}^{2}}$

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

$\frac{6 w \sqrt{w}}{5 w^{\frac{1}{2} \cdot 2}}$

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

$\frac{6 w \sqrt{w}}{5 w^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{6 w \sqrt{w}}{5 w^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{6 w \sqrt{w}}{5 w^{1}}$

Simplify.

$\frac{6 w \sqrt{w}}{5 w}$

Step 4

Cancel the common factor of $w$ .

Cancel the common factor.

$\frac{6 w \sqrt{w}}{5 w}$

Rewrite the expression.

$\frac{6 \sqrt{w}}{5}$