Finite Math Examples

$64^{\frac{1}{2}} - 2 (7 \sqrt{3 + 9})$

Step 1

Rewrite $64$ as $8^{2}$ .

${(8^{2})}^{\frac{1}{2}} - 2 (7 \sqrt{3 + 9})$

Step 2

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

$8^{2 (\frac{1}{2})} - 2 (7 \sqrt{3 + 9})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$8^{2 (\frac{1}{2})} - 2 (7 \sqrt{3 + 9})$

Step 3.2

Rewrite the expression.

$8^{1} - 2 (7 \sqrt{3 + 9})$

$8^{1} - 2 (7 \sqrt{3 + 9})$

Step 4

Evaluate the exponent.

$8 - 2 (7 \sqrt{3 + 9})$

Step 5

Add $3$ and $9$ .

$8 - 2 (7 \sqrt{12})$

Step 6

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 6.1

Factor $4$ out of $12$ .

$8 - 2 (7 \sqrt{4 (3)})$

Step 6.2

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

$8 - 2 (7 \sqrt{2^{2} \cdot 3})$

$8 - 2 (7 \sqrt{2^{2} \cdot 3})$

Step 7

Pull terms out from under the radical.

$8 - 2 (7 (2 \sqrt{3}))$

Step 8

Multiply $2$ by $7$ .

$8 - 2 (14 \sqrt{3})$

Step 9

Multiply $14$ by $- 2$ .

$8 - 28 \sqrt{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$8 - 28 \sqrt{3}$

Decimal Form:

$- 40.49742261 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$