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

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{10}$

Decimal Form:

$31.62277660 \dots$

Related Questions