Basic Math Examples

$4 \sqrt{5} - \frac{1}{2} \cdot \sqrt{20} + \sqrt{125} - \sqrt{1445}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$4 \sqrt{5} - \frac{1}{2} \cdot \sqrt{4 (5)} + \sqrt{125} - \sqrt{1445}$

Step 1.1.2

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

$4 \sqrt{5} - \frac{1}{2} \cdot \sqrt{2^{2} \cdot 5} + \sqrt{125} - \sqrt{1445}$

Step 1.2

Pull terms out from under the radical.

$4 \sqrt{5} - \frac{1}{2} \cdot (2 \sqrt{5}) + \sqrt{125} - \sqrt{1445}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$4 \sqrt{5} + \frac{- 1}{2} \cdot (2 \sqrt{5}) + \sqrt{125} - \sqrt{1445}$

Step 1.3.2

Factor $2$ out of $2 \sqrt{5}$ .

$4 \sqrt{5} + \frac{- 1}{2} \cdot (2 (\sqrt{5})) + \sqrt{125} - \sqrt{1445}$

Step 1.3.3

Cancel the common factor.

$4 \sqrt{5} + \frac{- 1}{2} \cdot (2 \sqrt{5}) + \sqrt{125} - \sqrt{1445}$

Step 1.3.4

Rewrite the expression.

$4 \sqrt{5} - 1 \cdot \sqrt{5} + \sqrt{125} - \sqrt{1445}$

Step 1.4

Rewrite $- 1 \sqrt{5}$ as $- \sqrt{5}$ .

$4 \sqrt{5} - \sqrt{5} + \sqrt{125} - \sqrt{1445}$

Step 1.5

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 1.5.1

Factor $25$ out of $125$ .

$4 \sqrt{5} - \sqrt{5} + \sqrt{25 (5)} - \sqrt{1445}$

Step 1.5.2

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

$4 \sqrt{5} - \sqrt{5} + \sqrt{5^{2} \cdot 5} - \sqrt{1445}$

Step 1.6

Pull terms out from under the radical.

$4 \sqrt{5} - \sqrt{5} + 5 \sqrt{5} - \sqrt{1445}$

Step 1.7

Rewrite $1445$ as $17^{2} \cdot 5$ .

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Step 1.7.1

Factor $289$ out of $1445$ .

$4 \sqrt{5} - \sqrt{5} + 5 \sqrt{5} - \sqrt{289 (5)}$

Step 1.7.2

Rewrite $289$ as $17^{2}$ .

$4 \sqrt{5} - \sqrt{5} + 5 \sqrt{5} - \sqrt{17^{2} \cdot 5}$

Step 1.8

Pull terms out from under the radical.

$4 \sqrt{5} - \sqrt{5} + 5 \sqrt{5} - (17 \sqrt{5})$

Step 1.9

Multiply $17$ by $- 1$ .

$4 \sqrt{5} - \sqrt{5} + 5 \sqrt{5} - 17 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $\sqrt{5}$ from $4 \sqrt{5}$ .

$3 \sqrt{5} + 5 \sqrt{5} - 17 \sqrt{5}$

Step 2.2

Add $3 \sqrt{5}$ and $5 \sqrt{5}$ .

$8 \sqrt{5} - 17 \sqrt{5}$

Step 2.3

Subtract $17 \sqrt{5}$ from $8 \sqrt{5}$ .

$- 9 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 9 \sqrt{5}$

Decimal Form:

$- 20.12461179 \dots$