Algebra Examples

$\sqrt{10} \cdot \sqrt{10^{3}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{10 \cdot 10^{3}}$

Step 2

Rewrite $10 \cdot 10^{3}$ as $1 \cdot 10^{4}$ .

$\sqrt{1 \cdot 10^{4}}$

Step 3

Rewrite $\sqrt{1 \cdot 10^{4}}$ as $\sqrt{1} \cdot \sqrt{10^{4}}$ .

$\sqrt{1} \cdot \sqrt{10^{4}}$

Step 4

Evaluate the root.

$1 \cdot \sqrt{10^{4}}$

Step 5

Rewrite $10^{4}$ as ${(10^{2})}^{2}$ .

$1 \cdot \sqrt{{(10^{2})}^{2}}$

Step 6

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

$1 \cdot 10^{2}$

Step 7

Multiply $10^{2}$ by $1$ .

$10^{2}$

Step 8

Raise $10$ to the power of $2$ .

$100$