Solve the Rational Equation for c square root of c=4

$\sqrt{c} = 4$

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

${\sqrt{c}}^{2} = 4^{2}$

Simplify each side of the equation.

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

${(c^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

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

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

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

$c^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$c^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

$c^{1} = 4^{2}$

Simplify.

$c = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$c = 16$