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

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

Move $1$ to the left side of the equation by subtracting it from both sides.

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

Add $1$ to both sides of the equation.

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

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

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

Simplify each side of the equation.

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Multiply the exponents in ${({(8 x - 5)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

One to any power is one.

$8 x - 5 = 1$

Solve for $x$ .

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

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Add $5$ to both sides of the equation.

$8 x = 1 + 5$

Add $1$ and $5$ .

$8 x = 6$

Divide each term by $8$ and simplify.

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Divide each term in $8 x = 6$ by $8$ .

$\frac{8 x}{8} = \frac{6}{8}$

Cancel the common factor of $8$ .

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Cancel the common factor.

$\frac{8 x}{8} = \frac{6}{8}$

Divide $x$ by $1$ .

$x = \frac{6}{8}$

Cancel the common factor of $6$ and $8$ .

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Factor $2$ out of $6$ .

$x = \frac{2 (3)}{8}$

Cancel the common factors.

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Factor $2$ out of $8$ .

$x = \frac{2 \cdot 3}{2 \cdot 4}$

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 4}$

Rewrite the expression.

$x = \frac{3}{4}$

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

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