Pre-Algebra Examples

$\frac{7 (52187) - 321 \cdot 1139}{\sqrt{7 (17467) - 321^{2}} \sqrt{7 (137884) - 1139^{2}}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $7$ by $52187$ .

$\frac{365309 - 321 \cdot 1139}{\sqrt{7 (17467) - 321^{2}} \sqrt{7 (137884) - 1139^{2}}}$

Step 1.2

Multiply $- 321$ by $1139$ .

$\frac{365309 - 365619}{\sqrt{7 (17467) - 321^{2}} \sqrt{7 (137884) - 1139^{2}}}$

Step 1.3

Subtract $365619$ from $365309$ .

$\frac{- 310}{\sqrt{7 (17467) - 321^{2}} \sqrt{7 (137884) - 1139^{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Combine using the product rule for radicals.

$\frac{- 310}{\sqrt{(7 (17467) - 321^{2}) (7 (137884) - 1139^{2})}}$

Step 2.2

Multiply $7$ by $17467$ .

$\frac{- 310}{\sqrt{(122269 - 321^{2}) (7 (137884) - 1139^{2})}}$

Step 2.3

Raise $321$ to the power of $2$ .

$\frac{- 310}{\sqrt{(122269 - 1 \cdot 103041) (7 (137884) - 1139^{2})}}$

Step 2.4

Multiply $- 1$ by $103041$ .

$\frac{- 310}{\sqrt{(122269 - 103041) (7 (137884) - 1139^{2})}}$

Step 2.5

Subtract $103041$ from $122269$ .

$\frac{- 310}{\sqrt{19228 (7 (137884) - 1139^{2})}}$

Step 2.6

Multiply $7$ by $137884$ .

$\frac{- 310}{\sqrt{19228 (965188 - 1139^{2})}}$

Step 2.7

Raise $1139$ to the power of $2$ .

$\frac{- 310}{\sqrt{19228 (965188 - 1 \cdot 1297321)}}$

Step 2.8

Multiply $- 1$ by $1297321$ .

$\frac{- 310}{\sqrt{19228 (965188 - 1297321)}}$

Step 2.9

Subtract $1297321$ from $965188$ .

$\frac{- 310}{\sqrt{19228 \cdot - 332133}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $19228$ by $- 332133$ .

$\frac{- 310}{\sqrt{- 6386253324}}$

Step 3.2

Rewrite $- 6386253324$ as $- 1 (6386253324)$ .

$\frac{- 310}{\sqrt{- 1 (6386253324)}}$

Step 3.3

Rewrite $\sqrt{- 1 (6386253324)}$ as $\sqrt{- 1} \cdot \sqrt{6386253324}$ .

$\frac{- 310}{\sqrt{- 1} \cdot \sqrt{6386253324}}$

Step 3.4

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{- 310}{i \cdot \sqrt{6386253324}}$

Step 3.5

Rewrite $6386253324$ as $2^{2} \cdot 1596563331$ .

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Step 3.5.1

Factor $4$ out of $6386253324$ .

$\frac{- 310}{i \cdot \sqrt{4 (1596563331)}}$

Step 3.5.2

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

$\frac{- 310}{i \cdot \sqrt{2^{2} \cdot 1596563331}}$

Step 3.6

Pull terms out from under the radical.

$\frac{- 310}{i \cdot (2 \sqrt{1596563331})}$

Step 3.7

Move $2$ to the left of $i$ .

$\frac{- 310}{2 i \sqrt{1596563331}}$

Step 4

Cancel the common factor of $- 310$ and $2$ .

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Step 4.1

Factor $2$ out of $- 310$ .

$\frac{2 \cdot - 155}{2 i \sqrt{1596563331}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2 i \sqrt{1596563331}$ .

$\frac{2 \cdot - 155}{2 (i \sqrt{1596563331})}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \cdot - 155}{2 (i \sqrt{1596563331})}$

Step 4.2.3

Rewrite the expression.

$\frac{- 155}{i \sqrt{1596563331}}$

Step 5

Multiply the numerator and denominator of $\frac{- 155}{39957.01854493 i}$ by the conjugate of $39957.01854493 i$ to make the denominator real.

$\frac{- 155}{39957.01854493 i} \cdot \frac{i}{i}$

Step 6

Multiply.

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Step 6.1

Combine.

$\frac{- 155 i}{39957.01854493 i i}$

Step 6.2

Simplify the denominator.

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Step 6.2.1

Add parentheses.

$\frac{- 155 i}{39957.01854493 (i i)}$

Step 6.2.2

Raise $i$ to the power of $1$ .

$\frac{- 155 i}{39957.01854493 (i^{1} i)}$

Step 6.2.3

Raise $i$ to the power of $1$ .

$\frac{- 155 i}{39957.01854493 (i^{1} i^{1})}$

Step 6.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 155 i}{39957.01854493 i^{1 + 1}}$

Step 6.2.5

Add $1$ and $1$ .

$\frac{- 155 i}{39957.01854493 i^{2}}$

Step 6.2.6

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 155 i}{39957.01854493 \cdot - 1}$

Step 7

Multiply $39957.01854493$ by $- 1$ .

$\frac{- 155 i}{- 39957.01854493}$

Step 8

Dividing two negative values results in a positive value.

$\frac{155 i}{39957.01854493}$

Step 9

Factor $155$ out of $155 i$ .

$\frac{155 (i)}{39957.01854493}$

Step 10

Factor $39957.01854493$ out of $39957.01854493$ .

$\frac{155 (i)}{39957.01854493 (1)}$

Step 11

Separate fractions.

$\frac{155}{39957.01854493} \cdot \frac{i}{1}$

Step 12

Divide $155$ by $39957.01854493$ .

$0.00387916 \frac{i}{1}$

Step 13

Divide $i$ by $1$ .

$0.00387916 i$