Finite Math Examples

$| 2 \sqrt{7} - \sqrt{63} | - (4 + \sqrt{7})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 1.1.1.1

Factor $9$ out of $63$ .

$| 2 \sqrt{7} - \sqrt{9 (7)} | - (4 + \sqrt{7})$

Step 1.1.1.2

Rewrite $9$ as $3^{2}$ .

$| 2 \sqrt{7} - \sqrt{3^{2} \cdot 7} | - (4 + \sqrt{7})$

Step 1.1.2

Pull terms out from under the radical.

$| 2 \sqrt{7} - (3 \sqrt{7}) | - (4 + \sqrt{7})$

Step 1.1.3

Multiply $3$ by $- 1$ .

$| 2 \sqrt{7} - 3 \sqrt{7} | - (4 + \sqrt{7})$

Step 1.2

Subtract $3 \sqrt{7}$ from $2 \sqrt{7}$ .

$| - \sqrt{7} | - (4 + \sqrt{7})$

Step 1.3

$- \sqrt{7}$ is approximately $- 2.64575131$ which is negative so negate $- \sqrt{7}$ and remove the absolute value

$\sqrt{7} - (4 + \sqrt{7})$

Step 1.4

Apply the distributive property.

$\sqrt{7} - 1 \cdot 4 - \sqrt{7}$

Step 1.5

Multiply $- 1$ by $4$ .

$\sqrt{7} - 4 - \sqrt{7}$

Step 2

Simplify by adding terms.

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Step 2.1

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

$0 - 4$

Step 2.2

Subtract $4$ from $0$ .

$- 4$