Algebra Examples

$x = \frac{\sqrt{2 y}}{26}$

Step 1

Rewrite the equation as $\frac{\sqrt{2 y}}{26} = x$ .

$\frac{\sqrt{2 y}}{26} = x$

Step 2

Multiply both sides by $26$ .

$\frac{\sqrt{2 y}}{26} \cdot 26 = x \cdot 26$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $26$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{\sqrt{2 y}}{26} \cdot 26 = x \cdot 26$

Step 3.1.1.2

Rewrite the expression.

$\sqrt{2 y} = x \cdot 26$

Step 3.2

Simplify the right side.

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Step 3.2.1

Move $26$ to the left of $x$ .

$\sqrt{2 y} = 26 x$

Step 4

Solve for $y$ .

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Step 4.1

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

${\sqrt{2 y}}^{2} = {(26 x)}^{2}$

Step 4.2

Simplify each side of the equation.

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Step 4.2.1

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

${({(2 y)}^{\frac{1}{2}})}^{2} = {(26 x)}^{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

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

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Step 4.2.2.1.1

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

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Step 4.2.2.1.1.1

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

${(2 y)}^{\frac{1}{2} \cdot 2} = {(26 x)}^{2}$

Step 4.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.2.1.1.2.1

Cancel the common factor.

${(2 y)}^{\frac{1}{2} \cdot 2} = {(26 x)}^{2}$

Step 4.2.2.1.1.2.2

Rewrite the expression.

${(2 y)}^{1} = {(26 x)}^{2}$

Step 4.2.2.1.2

Simplify.

$2 y = {(26 x)}^{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify ${(26 x)}^{2}$ .

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Step 4.2.3.1.1

Apply the product rule to $26 x$ .

$2 y = 26^{2} x^{2}$

Step 4.2.3.1.2

Raise $26$ to the power of $2$ .

$2 y = 676 x^{2}$

Step 4.3

Divide each term in $2 y = 676 x^{2}$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 y = 676 x^{2}$ by $2$ .

$\frac{2 y}{2} = \frac{676 x^{2}}{2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{676 x^{2}}{2}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{676 x^{2}}{2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $676$ and $2$ .

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Step 4.3.3.1.1

Factor $2$ out of $676 x^{2}$ .

$y = \frac{2 (338 x^{2})}{2}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (338 x^{2})}{2 (1)}$

Step 4.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 (338 x^{2})}{2 \cdot 1}$

Step 4.3.3.1.2.3

Rewrite the expression.

$y = \frac{338 x^{2}}{1}$

Step 4.3.3.1.2.4

Divide $338 x^{2}$ by $1$ .

$y = 338 x^{2}$