Solve for y square root of 2y-5+4=8

$\sqrt{2 y - 5} + 4 = 8$

Step 1

Move all terms not containing $\sqrt{2 y - 5}$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$\sqrt{2 y - 5} = 8 - 4$

Subtract $4$ from $8$ .

$\sqrt{2 y - 5} = 4$

Step 2

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

${\sqrt{2 y - 5}}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 y - 5}$ as ${(2 y - 5)}^{\frac{1}{2}}$ .

${({(2 y - 5)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

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

Multiply the exponents in ${({(2 y - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(2 y - 5)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 y - 5)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(2 y - 5)}^{1} = 4^{2}$

Simplify.

$2 y - 5 = 4^{2}$

Simplify the right side.

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

$2 y - 5 = 16$

Step 4

Solve for $y$ .

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

Add $5$ to both sides of the equation.

$2 y = 16 + 5$

Add $16$ and $5$ .

$2 y = 21$

Divide each term in $2 y = 21$ by $2$ and simplify.

Divide each term in $2 y = 21$ by $2$ .

$\frac{2 y}{2} = \frac{21}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{21}{2}$

Divide $y$ by $1$ .

$y = \frac{21}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{21}{2}$

Decimal Form:

$y = 10.5$

Mixed Number Form:

$y = 10 \frac{1}{2}$

Solve for y square root of 2y-5+4=8

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