Solve for y 4.820^2 = square root of 779.4y

${4.82}^{2} = \sqrt{779.4 y}$

Step 1

Rewrite the equation as $\sqrt{779.4 y} = {4.82}^{2}$ .

$\sqrt{779.4 y} = {4.82}^{2}$

Step 2

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

${\sqrt{779.4 y}}^{2} = {({4.82}^{2})}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{779.4 y}$ as ${(779.4 y)}^{\frac{1}{2}}$ .

${({(779.4 y)}^{\frac{1}{2}})}^{2} = {({4.82}^{2})}^{2}$

Simplify the left side.

Simplify ${({(779.4 y)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(779.4 y)}^{\frac{1}{2}})}^{2}$ .

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

${(779.4 y)}^{\frac{1}{2} \cdot 2} = {({4.82}^{2})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(779.4 y)}^{\frac{1}{2} \cdot 2} = {({4.82}^{2})}^{2}$

Rewrite the expression.

${(779.4 y)}^{1} = {({4.82}^{2})}^{2}$

Simplify.

$779.4 y = {({4.82}^{2})}^{2}$

Simplify the right side.

Simplify ${({4.82}^{2})}^{2}$ .

Multiply the exponents in ${({4.82}^{2})}^{2}$ .

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

$779.4 y = {4.82}^{2 \cdot 2}$

Multiply $2$ by $2$ .

$779.4 y = {4.82}^{4}$

Raise $4.82$ to the power of $4$ .

$779.4 y = 539.74440976$

Step 4

Divide each term in $779.4 y = 539.74440976$ by $779.4$ and simplify.

Divide each term in $779.4 y = 539.74440976$ by $779.4$ .

$\frac{779.4 y}{779.4} = \frac{539.74440976}{779.4}$

Simplify the left side.

Cancel the common factor of $779.4$ .

Cancel the common factor.

$\frac{779.4 y}{779.4} = \frac{539.74440976}{779.4}$

Divide $y$ by $1$ .

$y = \frac{539.74440976}{779.4}$

Simplify the right side.

Divide $539.74440976$ by $779.4$ .

$y = 0.69251271$