Solve by Factoring square root of 8x+1=5

$\sqrt{8 x + 1} = 5$

Step 1

Subtract $5$ from both sides of the equation.

$\sqrt{8 x + 1} - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$\sqrt{8 x + 1} = 5$

Step 3

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

${\sqrt{8 x + 1}}^{2} = 5^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x + 1}$ as ${(8 x + 1)}^{\frac{1}{2}}$ .

${({(8 x + 1)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(8 x + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(8 x + 1)}^{\frac{1}{2}})}^{2}$ .

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

${(8 x + 1)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 x + 1)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(8 x + 1)}^{1} = 5^{2}$

Simplify.

$8 x + 1 = 5^{2}$

Simplify the right side.

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

$8 x + 1 = 25$

Step 5

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$8 x = 25 - 1$

Subtract $1$ from $25$ .

$8 x = 24$

Divide each term in $8 x = 24$ by $8$ and simplify.

Divide each term in $8 x = 24$ by $8$ .

$\frac{8 x}{8} = \frac{24}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{24}{8}$

Divide $x$ by $1$ .

$x = \frac{24}{8}$

Simplify the right side.

Divide $24$ by $8$ .

$x = 3$

Solve by Factoring square root of 8x+1=5

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