Basic Math Examples

$3^{2} + 2 \cdot 5^{2} - 50 \div \sqrt{25}$

Step 1

Find the common denominator.

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Step 1.1

Write $3^{2}$ as a fraction with denominator $1$ .

$\frac{3^{2}}{1} + 2 \cdot 5^{2} - 50 \div \sqrt{25}$

Step 1.2

Multiply $\frac{3^{2}}{1}$ by $\frac{\sqrt{25}}{\sqrt{25}}$ .

$\frac{3^{2}}{1} \cdot \frac{\sqrt{25}}{\sqrt{25}} + 2 \cdot 5^{2} - 50 \div \sqrt{25}$

Step 1.3

Multiply $\frac{3^{2}}{1}$ by $\frac{\sqrt{25}}{\sqrt{25}}$ .

$\frac{3^{2} \sqrt{25}}{\sqrt{25}} + 2 \cdot 5^{2} - 50 \div \sqrt{25}$

Step 1.4

Write $2 \cdot 5^{2}$ as a fraction with denominator $1$ .

$\frac{3^{2} \sqrt{25}}{\sqrt{25}} + \frac{2 \cdot 5^{2}}{1} - 50 \div \sqrt{25}$

Step 1.5

Multiply $\frac{2 \cdot 5^{2}}{1}$ by $\frac{\sqrt{25}}{\sqrt{25}}$ .

$\frac{3^{2} \sqrt{25}}{\sqrt{25}} + \frac{2 \cdot 5^{2}}{1} \cdot \frac{\sqrt{25}}{\sqrt{25}} - 50 \div \sqrt{25}$

Step 1.6

Multiply $\frac{2 \cdot 5^{2}}{1}$ by $\frac{\sqrt{25}}{\sqrt{25}}$ .

$\frac{3^{2} \sqrt{25}}{\sqrt{25}} + \frac{2 \cdot 5^{2} \sqrt{25}}{\sqrt{25}} - 50 \div \sqrt{25}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{3^{2} \sqrt{25} + 2 \cdot 5^{2} \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2

Simplify each term.

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Step 2.2.1

Raise $3$ to the power of $2$ .

$\frac{9 \sqrt{25} + 2 \cdot 5^{2} \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2.2

Rewrite $25$ as $5^{2}$ .

$\frac{9 \sqrt{5^{2}} + 2 \cdot 5^{2} \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2.3

Pull terms out from under the radical, assuming positive real numbers.

$\frac{9 \cdot 5 + 2 \cdot 5^{2} \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2.4

Multiply $9$ by $5$ .

$\frac{45 + 2 \cdot 5^{2} \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2.5

Raise $5$ to the power of $2$ .

$\frac{45 + 2 \cdot 25 \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2.6

Multiply $2$ by $25$ .

$\frac{45 + 50 \sqrt{25} - 50}{\sqrt{25}}$

Step 2.2.7

Rewrite $25$ as $5^{2}$ .

$\frac{45 + 50 \sqrt{5^{2}} - 50}{\sqrt{25}}$

Step 2.2.8

Pull terms out from under the radical, assuming positive real numbers.

$\frac{45 + 50 \cdot 5 - 50}{\sqrt{25}}$

Step 2.2.9

Multiply $50$ by $5$ .

$\frac{45 + 250 - 50}{\sqrt{25}}$

Step 2.3

Simplify by adding and subtracting.

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Step 2.3.1

Add $45$ and $250$ .

$\frac{295 - 50}{\sqrt{25}}$

Step 2.3.2

Subtract $50$ from $295$ .

$\frac{245}{\sqrt{25}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

$\frac{245}{\sqrt{5^{2}}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{245}{5}$

Step 4

Divide $245$ by $5$ .

$49$