Pre-Algebra Examples

$C (25000) = \frac{10 \sqrt{25000} + 0.7 \sqrt{25000^{3}} - 0}{\sqrt{25000}}$

Step 1

Simplify.

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Step 1.1

Rewrite $25000$ as $50^{2} \cdot 10$ .

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Step 1.1.1

Factor $2500$ out of $25000$ .

$C (25000) = \frac{10 \sqrt{2500 (10)} + 0.7 \sqrt{25000^{3}} - 0}{\sqrt{25000}}$

Step 1.1.2

Rewrite $2500$ as $50^{2}$ .

$C (25000) = \frac{10 \sqrt{50^{2} \cdot 10} + 0.7 \sqrt{25000^{3}} - 0}{\sqrt{25000}}$

Step 1.2

Pull terms out from under the radical.

$C (25000) = \frac{10 (50 \sqrt{10}) + 0.7 \sqrt{25000^{3}} - 0}{\sqrt{25000}}$

Step 1.3

Multiply $50$ by $10$ .

$C (25000) = \frac{500 \sqrt{10} + 0.7 \sqrt{25000^{3}} - 0}{\sqrt{25000}}$

Step 1.4

Raise $25000$ to the power of $3$ .

$C (25000) = \frac{500 \sqrt{10} + 0.7 \sqrt{15625000000000} - 0}{\sqrt{25000}}$

Step 1.5

Rewrite $15625000000000$ as $1250000^{2} \cdot 10$ .

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Step 1.5.1

Factor $1562500000000$ out of $15625000000000$ .

$C (25000) = \frac{500 \sqrt{10} + 0.7 \sqrt{1562500000000 (10)} - 0}{\sqrt{25000}}$

Step 1.5.2

Rewrite $1562500000000$ as $1250000^{2}$ .

$C (25000) = \frac{500 \sqrt{10} + 0.7 \sqrt{1250000^{2} \cdot 10} - 0}{\sqrt{25000}}$

Step 1.6

Pull terms out from under the radical.

$C (25000) = \frac{500 \sqrt{10} + 0.7 (1250000 \sqrt{10}) - 0}{\sqrt{25000}}$

Step 1.7

Multiply $0.7 (1250000 \sqrt{10})$ .

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Step 1.7.1

Multiply $1250000$ by $0.7$ .

$C (25000) = \frac{500 \sqrt{10} + 875000 \sqrt{10} - 0}{\sqrt{25000}}$

Step 1.7.2

Multiply $875000$ by $\sqrt{10}$ .

$C (25000) = \frac{500 \sqrt{10} + 2766992.95264733 - 0}{\sqrt{25000}}$

Step 1.8

Multiply $- 1$ by $0$ .

$C (25000) = \frac{500 \sqrt{10} + 2766992.95264733 + 0}{\sqrt{25000}}$

Step 1.9

Simplify the numerator.

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Step 1.9.1

Add $500 \sqrt{10} + 2766992.95264733$ and $0$ .

$C (25000) = \frac{500 \sqrt{10} + 2766992.95264733}{\sqrt{25000}}$

Step 1.9.2

Add $500 \sqrt{10}$ and $2766992.95264733$ .

$C (25000) = \frac{2768574.09147741}{\sqrt{25000}}$

Step 1.10

Simplify the denominator.

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Step 1.10.1

Rewrite $25000$ as $50^{2} \cdot 10$ .

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Step 1.10.1.1

Factor $2500$ out of $25000$ .

$C (25000) = \frac{2768574.09147741}{\sqrt{2500 (10)}}$

Step 1.10.1.2

Rewrite $2500$ as $50^{2}$ .

$C (25000) = \frac{2768574.09147741}{\sqrt{50^{2} \cdot 10}}$

Step 1.10.2

Pull terms out from under the radical.

$C (25000) = \frac{2768574.09147741}{50 \sqrt{10}}$

Step 1.11

Multiply $\frac{2768574.09147741}{50 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$C (25000) = \frac{2768574.09147741}{50 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 1.12

Combine and simplify the denominator.

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Step 1.12.1

Multiply $\frac{2768574.09147741}{50 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 \sqrt{10} \sqrt{10}}$

Step 1.12.2

Move $\sqrt{10}$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 (\sqrt{10} \sqrt{10})}$

Step 1.12.3

Raise $\sqrt{10}$ to the power of $1$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 ({\sqrt{10}}^{1} \sqrt{10})}$

Step 1.12.4

Raise $\sqrt{10}$ to the power of $1$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

Step 1.12.5

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

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 {\sqrt{10}}^{1 + 1}}$

Step 1.12.6

Add $1$ and $1$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 {\sqrt{10}}^{2}}$

Step 1.12.7

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 1.12.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 {(10^{\frac{1}{2}})}^{2}}$

Step 1.12.7.2

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

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 \cdot 10^{\frac{1}{2} \cdot 2}}$

Step 1.12.7.3

Combine $\frac{1}{2}$ and $2$ .

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 \cdot 10^{\frac{2}{2}}}$

Step 1.12.7.4

Cancel the common factor of $2$ .

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Step 1.12.7.4.1

Cancel the common factor.

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 \cdot 10^{\frac{2}{2}}}$

Step 1.12.7.4.2

Rewrite the expression.

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 \cdot 10^{1}}$

Step 1.12.7.5

Evaluate the exponent.

$C (25000) = \frac{2768574.09147741 \sqrt{10}}{50 \cdot 10}$

Step 1.13

Multiply $2768574.09147741$ by $\sqrt{10}$ .

$C (25000) = \frac{8755000}{50 \cdot 10}$

Step 1.14

Multiply $50$ by $10$ .

$C (25000) = \frac{8755000}{500}$

Step 1.15

Divide $8755000$ by $500$ .

$C (25000) = 17510$

Step 2

Divide each term in $C (25000) = 17510$ by $25000$ and simplify.

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Step 2.1

Divide each term in $C (25000) = 17510$ by $25000$ .

$\frac{C (25000)}{25000} = \frac{17510}{25000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $25000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{C \cdot 25000}{25000} = \frac{17510}{25000}$

Step 2.2.1.2

Divide $C$ by $1$ .

$C = \frac{17510}{25000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $17510$ by $25000$ .

$C = 0.7004$