Algebra Examples

$10^{3} - 5 \sqrt{3^{2} + 4^{2}} - (9 - 12) (7 - 12)$

Step 1

Simplify each term.

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Step 1.1

Raise $10$ to the power of $3$ .

$1000 - 5 \sqrt{3^{2} + 4^{2}} - (9 - 12) (7 - 12)$

Step 1.2

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

$1000 - 5 \sqrt{9 + 4^{2}} - (9 - 12) (7 - 12)$

Step 1.3

Raise $4$ to the power of $2$ .

$1000 - 5 \sqrt{9 + 16} - (9 - 12) (7 - 12)$

Step 1.4

Add $9$ and $16$ .

$1000 - 5 \sqrt{25} - (9 - 12) (7 - 12)$

Step 1.5

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

$1000 - 5 \sqrt{5^{2}} - (9 - 12) (7 - 12)$

Step 1.6

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

$1000 - 5 \cdot 5 - (9 - 12) (7 - 12)$

Step 1.7

Multiply $- 5$ by $5$ .

$1000 - 25 - (9 - 12) (7 - 12)$

Step 1.8

Subtract $12$ from $9$ .

$1000 - 25 - - 3 (7 - 12)$

Step 1.9

Multiply $- 1$ by $- 3$ .

$1000 - 25 + 3 (7 - 12)$

Step 1.10

Subtract $12$ from $7$ .

$1000 - 25 + 3 \cdot - 5$

Step 1.11

Multiply $3$ by $- 5$ .

$1000 - 25 - 15$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $25$ from $1000$ .

$975 - 15$

Step 2.2

Subtract $15$ from $975$ .

$960$