Solve for h 12.1 = square root of 9.6^2+h^2

$12.1 = \sqrt{{9.6}^{2} + h^{2}}$

Rewrite the equation as $\sqrt{{9.6}^{2} + h^{2}} = 12.1$ .

$\sqrt{{9.6}^{2} + h^{2}} = 12.1$

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

${\sqrt{{9.6}^{2} + h^{2}}}^{2} = {12.1}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{{9.6}^{2} + h^{2}}$ as ${({9.6}^{2} + h^{2})}^{\frac{1}{2}}$ .

${({({9.6}^{2} + h^{2})}^{\frac{1}{2}})}^{2} = {12.1}^{2}$

Simplify the left side.

Simplify ${({({9.6}^{2} + h^{2})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({({9.6}^{2} + h^{2})}^{\frac{1}{2}})}^{2}$ .

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

${({9.6}^{2} + h^{2})}^{\frac{1}{2} \cdot 2} = {12.1}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${({9.6}^{2} + h^{2})}^{\frac{1}{2} \cdot 2} = {12.1}^{2}$

Rewrite the expression.

${({9.6}^{2} + h^{2})}^{1} = {12.1}^{2}$

Raise $9.6$ to the power of $2$ .

${(92.16 + h^{2})}^{1} = {12.1}^{2}$

Simplify.

$92.16 + h^{2} = {12.1}^{2}$

Simplify the right side.

Raise $12.1$ to the power of $2$ .

$92.16 + h^{2} = 146.41$

Solve for $h$ .

Move all terms not containing $h$ to the right side of the equation.

Subtract $92.16$ from both sides of the equation.

$h^{2} = 146.41 - 92.16$

Subtract $92.16$ from $146.41$ .

$h^{2} = 54.25$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$h = \pm \sqrt{54.25}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$h = \sqrt{54.25}$

Next, use the negative value of the $\pm$ to find the second solution.

$h = - \sqrt{54.25}$

The complete solution is the result of both the positive and negative portions of the solution.

$h = \sqrt{54.25}, - \sqrt{54.25}$

The result can be shown in multiple forms.

Exact Form:

$h = \sqrt{54.25}, - \sqrt{54.25}$

Decimal Form:

$h = 7.36545993 \dots, - 7.36545993 \dots$