Solve for y square root of 2x+y-3z=5

$\sqrt{2 x + y - 3 z} = 5$

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

${\sqrt{2 x + y - 3 z}}^{2} = 5^{2}$

Simplify each side of the equation.

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

${({(2 x + y - 3 z)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(2 x + y - 3 z)}^{\frac{1}{2}})}^{2}$ .

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

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

${(2 x + y - 3 z)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x + y - 3 z)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(2 x + y - 3 z)}^{1} = 5^{2}$

Simplify.

$2 x + y - 3 z = 5^{2}$

Simplify the right side.

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

$2 x + y - 3 z = 25$

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

Subtract $2 x$ from both sides of the equation.

$y - 3 z = 25 - 2 x$

Add $3 z$ to both sides of the equation.

$y = 25 - 2 x + 3 z$