Basic Math Examples

$35 \cdot (20 \sqrt{10}) + \frac{50 \cdot 2800}{20 \sqrt{10}}$

Step 1

Multiply $50$ by $2800$ .

$35 \cdot (20 \sqrt{10}) + \frac{140000}{20 \sqrt{10}}$

Step 2

Simplify each term.

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Step 2.1

Multiply $20$ by $35$ .

$700 \sqrt{10} + \frac{140000}{20 \sqrt{10}}$

Step 2.2

Cancel the common factor of $140000$ and $20$ .

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Step 2.2.1

Factor $20$ out of $140000$ .

$700 \sqrt{10} + \frac{20 \cdot 7000}{20 \sqrt{10}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $20$ out of $20 \sqrt{10}$ .

$700 \sqrt{10} + \frac{20 \cdot 7000}{20 (\sqrt{10})}$

Step 2.2.2.2

Cancel the common factor.

$700 \sqrt{10} + \frac{20 \cdot 7000}{20 \sqrt{10}}$

Step 2.2.2.3

Rewrite the expression.

$700 \sqrt{10} + \frac{7000}{\sqrt{10}}$

Step 2.3

Multiply $\frac{7000}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$700 \sqrt{10} + \frac{7000}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 2.4

Combine and simplify the denominator.

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Step 2.4.1

Multiply $\frac{7000}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{\sqrt{10} \sqrt{10}}$

Step 2.4.2

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

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Step 2.4.3

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

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Step 2.4.4

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

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Step 2.4.5

Add $1$ and $1$ .

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{{\sqrt{10}}^{2}}$

Step 2.4.6

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

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Step 2.4.6.1

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

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Step 2.4.6.2

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

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

Step 2.4.6.3

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

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{10^{\frac{2}{2}}}$

Step 2.4.6.4

Cancel the common factor of $2$ .

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Step 2.4.6.4.1

Cancel the common factor.

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{10^{\frac{2}{2}}}$

Step 2.4.6.4.2

Rewrite the expression.

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{10^{1}}$

Step 2.4.6.5

Evaluate the exponent.

$700 \sqrt{10} + \frac{7000 \sqrt{10}}{10}$

Step 2.5

Cancel the common factor of $7000$ and $10$ .

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Step 2.5.1

Factor $10$ out of $7000 \sqrt{10}$ .

$700 \sqrt{10} + \frac{10 (700 \sqrt{10})}{10}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $10$ out of $10$ .

$700 \sqrt{10} + \frac{10 (700 \sqrt{10})}{10 (1)}$

Step 2.5.2.2

Cancel the common factor.

$700 \sqrt{10} + \frac{10 (700 \sqrt{10})}{10 \cdot 1}$

Step 2.5.2.3

Rewrite the expression.

$700 \sqrt{10} + \frac{700 \sqrt{10}}{1}$

Step 2.5.2.4

Divide $700 \sqrt{10}$ by $1$ .

$700 \sqrt{10} + 700 \sqrt{10}$

Step 3

Add $700 \sqrt{10}$ and $700 \sqrt{10}$ .

$1400 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$1400 \sqrt{10}$

Decimal Form:

$4427.18872423 \dots$