Basic Math Examples

$\sqrt{A - 1} - \frac{4}{4^{2}} = \frac{1}{2}$

Step 1

Solve for $\sqrt{A - 1}$ .

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Step 1.1

Cancel the common factor of $4$ and $4^{2}$ .

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Step 1.1.1

Factor $4$ out of $4$ .

$\sqrt{A - 1} - \frac{4 (1)}{4^{2}} = \frac{1}{2}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $4$ out of $4^{2}$ .

$\sqrt{A - 1} - \frac{4 (1)}{4 \cdot 4} = \frac{1}{2}$

Step 1.1.2.2

Cancel the common factor.

$\sqrt{A - 1} - \frac{4 \cdot 1}{4 \cdot 4} = \frac{1}{2}$

Step 1.1.2.3

Rewrite the expression.

$\sqrt{A - 1} - \frac{1}{4} = \frac{1}{2}$

Step 1.2

Move all terms not containing $\sqrt{A - 1}$ to the right side of the equation.

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Step 1.2.1

Add $\frac{1}{4}$ to both sides of the equation.

$\sqrt{A - 1} = \frac{1}{2} + \frac{1}{4}$

Step 1.2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\sqrt{A - 1} = \frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4}$

Step 1.2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\sqrt{A - 1} = \frac{2}{2 \cdot 2} + \frac{1}{4}$

Step 1.2.3.2

Multiply $2$ by $2$ .

$\sqrt{A - 1} = \frac{2}{4} + \frac{1}{4}$

Step 1.2.4

Combine the numerators over the common denominator.

$\sqrt{A - 1} = \frac{2 + 1}{4}$

Step 1.2.5

Add $2$ and $1$ .

$\sqrt{A - 1} = \frac{3}{4}$

Step 2

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

${\sqrt{A - 1}}^{2} = {(\frac{3}{4})}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

${({(A - 1)}^{\frac{1}{2}})}^{2} = {(\frac{3}{4})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

${(A - 1)}^{\frac{1}{2} \cdot 2} = {(\frac{3}{4})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(A - 1)}^{\frac{1}{2} \cdot 2} = {(\frac{3}{4})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(A - 1)}^{1} = {(\frac{3}{4})}^{2}$

Step 3.2.1.2

Simplify.

$A - 1 = {(\frac{3}{4})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(\frac{3}{4})}^{2}$ .

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Step 3.3.1.1

Apply the product rule to $\frac{3}{4}$ .

$A - 1 = \frac{3^{2}}{4^{2}}$

Step 3.3.1.2

Raise $3$ to the power of $2$ .

$A - 1 = \frac{9}{4^{2}}$

Step 3.3.1.3

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

$A - 1 = \frac{9}{16}$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$A = \frac{9}{16} + 1$

Step 4.2

Write $1$ as a fraction with a common denominator.

$A = \frac{9}{16} + \frac{16}{16}$

Step 4.3

Combine the numerators over the common denominator.

$A = \frac{9 + 16}{16}$

Step 4.4

Add $9$ and $16$ .

$A = \frac{25}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$A = \frac{25}{16}$

Decimal Form:

$A = 1.5625$

Mixed Number Form:

$A = 1 \frac{9}{16}$