Simplify - square root of 1000

$- \sqrt{1000}$

Step 1

Rewrite $1000$ as $10^{2} \cdot 10$ .

Factor $100$ out of $1000$ .

$- \sqrt{100 (10)}$

Rewrite $100$ as $10^{2}$ .

$- \sqrt{10^{2} \cdot 10}$

$- \sqrt{10^{2} \cdot 10}$

Step 2

Pull terms out from under the radical.

$- (10 \sqrt{10})$

Step 3

Multiply $10$ by $- 1$ .

$- 10 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 10 \sqrt{10}$

Decimal Form:

$- 31.62277660 \dots$

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