Solve for h 15 = square root of 2(9.8)h

$15 = \sqrt{2 (9.8) h}$

Rewrite the equation as $\sqrt{2 (9.8) h} = 15$ .

$\sqrt{2 (9.8) h} = 15$

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

${\sqrt{2 (9.8) h}}^{2} = 15^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 (9.8) h}$ as ${(2 (9.8) h)}^{\frac{1}{2}}$ .

${({(2 (9.8) h)}^{\frac{1}{2}})}^{2} = 15^{2}$

Simplify the left side.

Simplify ${({(2 (9.8) h)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 (9.8) h)}^{\frac{1}{2}})}^{2}$ .

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

${(2 (9.8) h)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 (9.8) h)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Rewrite the expression.

${(2 (9.8) h)}^{1} = 15^{2}$

Multiply $2$ by $9.8$ .

${(19.6 h)}^{1} = 15^{2}$

Simplify.

$19.6 h = 15^{2}$

Simplify the right side.

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

$19.6 h = 225$

Divide each term in $19.6 h = 225$ by $19.6$ and simplify.

Divide each term in $19.6 h = 225$ by $19.6$ .

$\frac{19.6 h}{19.6} = \frac{225}{19.6}$

Simplify the left side.

Cancel the common factor of $19.6$ .

Cancel the common factor.

$\frac{19.6 h}{19.6} = \frac{225}{19.6}$

Divide $h$ by $1$ .

$h = \frac{225}{19.6}$

Simplify the right side.

Divide $225$ by $19.6$ .

$h = 11.47959183$