Solve for y 5 square root of y-2=10

$5 \sqrt{y - 2} = 10$

Step 1

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

${(5 \sqrt{y - 2})}^{2} = 10^{2}$

Step 2

Simplify each side of the equation.

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

${(5 {(y - 2)}^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

Simplify ${(5 {(y - 2)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $5 {(y - 2)}^{\frac{1}{2}}$ .

$5^{2} {({(y - 2)}^{\frac{1}{2}})}^{2} = 10^{2}$

Raise $5$ to the power of $2$ .

$25 {({(y - 2)}^{\frac{1}{2}})}^{2} = 10^{2}$

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

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

$25 {(y - 2)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 {(y - 2)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

$25 {(y - 2)}^{1} = 10^{2}$

Simplify.

$25 (y - 2) = 10^{2}$

Apply the distributive property.

$25 y + 25 \cdot - 2 = 10^{2}$

Multiply $25$ by $- 2$ .

$25 y - 50 = 10^{2}$

Simplify the right side.

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

$25 y - 50 = 100$

Step 3

Solve for $y$ .

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

Add $50$ to both sides of the equation.

$25 y = 100 + 50$

Add $100$ and $50$ .

$25 y = 150$

Divide each term in $25 y = 150$ by $25$ and simplify.

Divide each term in $25 y = 150$ by $25$ .

$\frac{25 y}{25} = \frac{150}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 y}{25} = \frac{150}{25}$

Divide $y$ by $1$ .

$y = \frac{150}{25}$

Simplify the right side.

Divide $150$ by $25$ .

$y = 6$

Solve for y 5 square root of y-2=10

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