Basic Math Examples

${(1 - \sqrt{\frac{9}{4}})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt{\frac{9}{4}}$ as $\frac{\sqrt{9}}{\sqrt{4}}$ .

${(1 - \frac{\sqrt{9}}{\sqrt{4}})}^{2}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $9$ as $3^{2}$ .

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

Step 1.2.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $4$ as $2^{2}$ .

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

Step 1.3.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2

Simplify the expression.

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Step 2.1

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

${(\frac{2}{2} - \frac{3}{2})}^{2}$

Step 2.2

Combine the numerators over the common denominator.

${(\frac{2 - 3}{2})}^{2}$

Step 2.3

Subtract $3$ from $2$ .

${(\frac{- 1}{2})}^{2}$

Step 2.4

Move the negative in front of the fraction.

${(- \frac{1}{2})}^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

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

${(- 1)}^{2} {(\frac{1}{2})}^{2}$

Step 3.2

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

${(- 1)}^{2} \frac{1^{2}}{2^{2}}$

Step 4

Raise $- 1$ to the power of $2$ .

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

Step 5

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

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

Step 6

One to any power is one.

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

Step 7

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

$\frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$