Finite Math Examples

$\frac{6 (1005) - 24 \cdot 240}{\sqrt{6 (106) - {(24)}^{2} \sqrt{6 (9826) - {(240)}^{2}}}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $6$ by $1005$ .

$\frac{6030 - 24 \cdot 240}{\sqrt{6 (106) - 24^{2} \sqrt{6 (9826) - 240^{2}}}}$

Step 1.2

Multiply $- 24$ by $240$ .

$\frac{6030 - 5760}{\sqrt{6 (106) - 24^{2} \sqrt{6 (9826) - 240^{2}}}}$

Step 1.3

Subtract $5760$ from $6030$ .

$\frac{270}{\sqrt{6 (106) - 24^{2} \sqrt{6 (9826) - 240^{2}}}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $6$ by $106$ .

$\frac{270}{\sqrt{636 - 24^{2} \sqrt{6 (9826) - 240^{2}}}}$

Step 2.2

Raise $24$ to the power of $2$ .

$\frac{270}{\sqrt{636 - 1 \cdot 576 \sqrt{6 (9826) - 240^{2}}}}$

Step 2.3

Multiply $- 1$ by $576$ .

$\frac{270}{\sqrt{636 - 576 \sqrt{6 (9826) - 240^{2}}}}$

Step 2.4

Multiply $6$ by $9826$ .

$\frac{270}{\sqrt{636 - 576 \sqrt{58956 - 240^{2}}}}$

Step 2.5

Raise $240$ to the power of $2$ .

$\frac{270}{\sqrt{636 - 576 \sqrt{58956 - 1 \cdot 57600}}}$

Step 2.6

Multiply $- 1$ by $57600$ .

$\frac{270}{\sqrt{636 - 576 \sqrt{58956 - 57600}}}$

Step 2.7

Subtract $57600$ from $58956$ .

$\frac{270}{\sqrt{636 - 576 \sqrt{1356}}}$

Step 2.8

Rewrite $1356$ as $2^{2} \cdot 339$ .

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Step 2.8.1

Factor $4$ out of $1356$ .

$\frac{270}{\sqrt{636 - 576 \sqrt{4 (339)}}}$

Step 2.8.2

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

$\frac{270}{\sqrt{636 - 576 \sqrt{2^{2} \cdot 339}}}$

Step 2.9

Pull terms out from under the radical.

$\frac{270}{\sqrt{636 - 576 (2 \sqrt{339})}}$

Step 2.10

Multiply $2$ by $- 576$ .

$\frac{270}{\sqrt{636 - 1152 \sqrt{339}}}$