Basic Math Examples

$4 \sqrt{175} - 4 \sqrt{20} - 4 \sqrt{125} - \sqrt{28}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $175$ as $5^{2} \cdot 7$ .

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Step 1.1.1

Factor $25$ out of $175$ .

$4 \sqrt{25 (7)} - 4 \sqrt{20} - 4 \sqrt{125} - \sqrt{28}$

Step 1.1.2

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

$4 \sqrt{5^{2} \cdot 7} - 4 \sqrt{20} - 4 \sqrt{125} - \sqrt{28}$

Step 1.2

Pull terms out from under the radical.

$4 (5 \sqrt{7}) - 4 \sqrt{20} - 4 \sqrt{125} - \sqrt{28}$

Step 1.3

Multiply $5$ by $4$ .

$20 \sqrt{7} - 4 \sqrt{20} - 4 \sqrt{125} - \sqrt{28}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $20$ .

$20 \sqrt{7} - 4 \sqrt{4 (5)} - 4 \sqrt{125} - \sqrt{28}$

Step 1.4.2

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

$20 \sqrt{7} - 4 \sqrt{2^{2} \cdot 5} - 4 \sqrt{125} - \sqrt{28}$

Step 1.5

Pull terms out from under the radical.

$20 \sqrt{7} - 4 (2 \sqrt{5}) - 4 \sqrt{125} - \sqrt{28}$

Step 1.6

Multiply $2$ by $- 4$ .

$20 \sqrt{7} - 8 \sqrt{5} - 4 \sqrt{125} - \sqrt{28}$

Step 1.7

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

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Step 1.7.1

Factor $25$ out of $125$ .

$20 \sqrt{7} - 8 \sqrt{5} - 4 \sqrt{25 (5)} - \sqrt{28}$

Step 1.7.2

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

$20 \sqrt{7} - 8 \sqrt{5} - 4 \sqrt{5^{2} \cdot 5} - \sqrt{28}$

Step 1.8

Pull terms out from under the radical.

$20 \sqrt{7} - 8 \sqrt{5} - 4 (5 \sqrt{5}) - \sqrt{28}$

Step 1.9

Multiply $5$ by $- 4$ .

$20 \sqrt{7} - 8 \sqrt{5} - 20 \sqrt{5} - \sqrt{28}$

Step 1.10

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 1.10.1

Factor $4$ out of $28$ .

$20 \sqrt{7} - 8 \sqrt{5} - 20 \sqrt{5} - \sqrt{4 (7)}$

Step 1.10.2

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

$20 \sqrt{7} - 8 \sqrt{5} - 20 \sqrt{5} - \sqrt{2^{2} \cdot 7}$

Step 1.11

Pull terms out from under the radical.

$20 \sqrt{7} - 8 \sqrt{5} - 20 \sqrt{5} - (2 \sqrt{7})$

Step 1.12

Multiply $2$ by $- 1$ .

$20 \sqrt{7} - 8 \sqrt{5} - 20 \sqrt{5} - 2 \sqrt{7}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 \sqrt{7}$ from $20 \sqrt{7}$ .

$18 \sqrt{7} - 8 \sqrt{5} - 20 \sqrt{5}$

Step 2.2

Subtract $20 \sqrt{5}$ from $- 8 \sqrt{5}$ .

$18 \sqrt{7} - 28 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{7} - 28 \sqrt{5}$

Decimal Form:

$- 14.98637977 \dots$