Solve for y 60=10 square root of y-3

$60 = 10 \sqrt{y - 3}$

Rewrite the equation as $10 \sqrt{y - 3} = 60$ .

$10 \sqrt{y - 3} = 60$

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

${(10 \sqrt{y - 3})}^{2} = 60^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y - 3}$ as ${(y - 3)}^{\frac{1}{2}}$ .

${(10 {(y - 3)}^{\frac{1}{2}})}^{2} = 60^{2}$

Simplify the left side.

Simplify ${(10 {(y - 3)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $10 {(y - 3)}^{\frac{1}{2}}$ .

$10^{2} {({(y - 3)}^{\frac{1}{2}})}^{2} = 60^{2}$

Raise $10$ to the power of $2$ .

$100 {({(y - 3)}^{\frac{1}{2}})}^{2} = 60^{2}$

Multiply the exponents in ${({(y - 3)}^{\frac{1}{2}})}^{2}$ .

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

$100 {(y - 3)}^{\frac{1}{2} \cdot 2} = 60^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$100 {(y - 3)}^{\frac{1}{2} \cdot 2} = 60^{2}$

Rewrite the expression.

$100 {(y - 3)}^{1} = 60^{2}$

Simplify.

$100 (y - 3) = 60^{2}$

Apply the distributive property.

$100 y + 100 \cdot - 3 = 60^{2}$

Multiply $100$ by $- 3$ .

$100 y - 300 = 60^{2}$

Simplify the right side.

Raise $60$ to the power of $2$ .

$100 y - 300 = 3600$

Solve for $y$ .

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

Add $300$ to both sides of the equation.

$100 y = 3600 + 300$

Add $3600$ and $300$ .

$100 y = 3900$

Divide each term in $100 y = 3900$ by $100$ and simplify.

Divide each term in $100 y = 3900$ by $100$ .

$\frac{100 y}{100} = \frac{3900}{100}$

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$\frac{100 y}{100} = \frac{3900}{100}$

Divide $y$ by $1$ .

$y = \frac{3900}{100}$

Simplify the right side.

Divide $3900$ by $100$ .

$y = 39$

Solve for y 60=10 square root of y-3

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