Evaluate log of 10 square root of 1000

$\log (10 \sqrt{1000})$

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

Factor $100$ out of $1000$ .

$\log (10 \sqrt{100 (10)})$

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

$\log (10 \sqrt{10^{2} \cdot 10})$

$\log (10 \sqrt{10^{2} \cdot 10})$

Pull terms out from under the radical.

$\log (10 (10 \sqrt{10}))$

Multiply $10$ by $10$ .

$\log (100 \sqrt{10})$

The result can be shown in multiple forms.

Exact Form:

$\log (100 \sqrt{10})$

Decimal Form:

$2.5$

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