Algebra Examples

$\sqrt{x} = \frac{1}{2}$

Step 1

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

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

Step 2

Simplify each side of the equation.

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.1.2

Simplify.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

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

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Step 2.3.1.1

Apply the product rule to $\frac{1}{2}$ .

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

Step 2.3.1.2

One to any power is one.

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

Step 2.3.1.3

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

$x = \frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$