Solve for h 15 = square root of h/16

$15 = \sqrt{\frac{h}{16}}$

Rewrite the equation as $\sqrt{\frac{h}{16}} = 15$ .

$\sqrt{\frac{h}{16}} = 15$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{h}{16}}}^{2} = 15^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{h}{16}}$ as ${(\frac{h}{16})}^{\frac{1}{2}}$ .

${({(\frac{h}{16})}^{\frac{1}{2}})}^{2} = 15^{2}$

Simplify the left side.

Simplify ${({(\frac{h}{16})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{h}{16})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{h}{16})}^{\frac{1}{2} \cdot 2} = 15^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{h}{16})}^{\frac{1}{2} \cdot 2} = 15^{2}$

Rewrite the expression.

${(\frac{h}{16})}^{1} = 15^{2}$

Simplify.

$\frac{h}{16} = 15^{2}$

Simplify the right side.

Raise $15$ to the power of $2$ .

$\frac{h}{16} = 225$

Solve for $h$ .

Multiply both sides of the equation by $16$ .

$16 \frac{h}{16} = 16 \cdot 225$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$16 \frac{h}{16} = 16 \cdot 225$

Rewrite the expression.

$h = 16 \cdot 225$

Simplify the right side.

Multiply $16$ by $225$ .

$h = 3600$