Basic Math Examples

$(- 8) + 8 \cdot \frac{3}{\sqrt{25}} \cdot \frac{3}{\sqrt{25}}$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

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

$- 8 + 8 \cdot \frac{3}{\sqrt{25}} \cdot \frac{3}{\sqrt{5^{2}}}$

Step 1.1.2

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

$- 8 + 8 \cdot \frac{3}{\sqrt{25}} \cdot \frac{3}{5}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

$- 8 + 8 \cdot \frac{3}{\sqrt{5^{2}}} \cdot \frac{3}{5}$

Step 1.2.2

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

$- 8 + 8 \cdot \frac{3}{5} \cdot \frac{3}{5}$

Step 1.3

Multiply $8 (\frac{3}{5})$ .

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Step 1.3.1

Combine $8$ and $\frac{3}{5}$ .

$- 8 + \frac{8 \cdot 3}{5} \cdot \frac{3}{5}$

Step 1.3.2

Multiply $8$ by $3$ .

$- 8 + \frac{24}{5} \cdot \frac{3}{5}$

Step 1.4

Multiply $\frac{24}{5} \cdot \frac{3}{5}$ .

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Step 1.4.1

Multiply $\frac{24}{5}$ by $\frac{3}{5}$ .

$- 8 + \frac{24 \cdot 3}{5 \cdot 5}$

Step 1.4.2

Multiply $24$ by $3$ .

$- 8 + \frac{72}{5 \cdot 5}$

Step 1.4.3

Multiply $5$ by $5$ .

$- 8 + \frac{72}{25}$

Step 2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$- 8 \cdot \frac{25}{25} + \frac{72}{25}$

Step 3

Combine $- 8$ and $\frac{25}{25}$ .

$\frac{- 8 \cdot 25}{25} + \frac{72}{25}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 25 + 72}{25}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 8$ by $25$ .

$\frac{- 200 + 72}{25}$

Step 5.2

Add $- 200$ and $72$ .

$\frac{- 128}{25}$

Step 6

Move the negative in front of the fraction.

$- \frac{128}{25}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{128}{25}$

Decimal Form:

$- 5.12$

Mixed Number Form:

$- 5 \frac{3}{25}$