Solve for r r = square root of (3v)/(ph)

$r = \sqrt{\frac{3 v}{p h}}$

Step 1

Rewrite $\sqrt{\frac{3 v}{p h}}$ as $\frac{\sqrt{3 v}}{\sqrt{p h}}$ .

$r = \frac{\sqrt{3 v}}{\sqrt{p h}}$

Step 2

Multiply $\frac{\sqrt{3 v}}{\sqrt{p h}}$ by $\frac{\sqrt{p h}}{\sqrt{p h}}$ .

$r = \frac{\sqrt{3 v}}{\sqrt{p h}} \cdot \frac{\sqrt{p h}}{\sqrt{p h}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3 v}}{\sqrt{p h}}$ by $\frac{\sqrt{p h}}{\sqrt{p h}}$ .

$r = \frac{\sqrt{3 v} \sqrt{p h}}{\sqrt{p h} \sqrt{p h}}$

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

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{\sqrt{p h}}^{1} \sqrt{p h}}$

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

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{\sqrt{p h}}^{1} {\sqrt{p h}}^{1}}$

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

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{\sqrt{p h}}^{1 + 1}}$

Add $1$ and $1$ .

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{\sqrt{p h}}^{2}}$

Rewrite ${\sqrt{p h}}^{2}$ as $p h$ .

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

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{({(p h)}^{\frac{1}{2}})}^{2}}$

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

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{(p h)}^{\frac{1}{2} \cdot 2}}$

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

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{(p h)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{(p h)}^{\frac{2}{2}}}$

Rewrite the expression.

$r = \frac{\sqrt{3 v} \sqrt{p h}}{{(p h)}^{1}}$

Simplify.

$r = \frac{\sqrt{3 v} \sqrt{p h}}{p h}$

Step 4

Combine using the product rule for radicals.

$r = \frac{\sqrt{3 v p h}}{p h}$