Algebra Examples

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

Step 1

Combine using the product rule for radicals.

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

Step 2

Multiply $10$ by $10^{3}$ by adding the exponents.

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Step 2.1

Multiply $10$ by $10^{3}$ .

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Step 2.1.1

Raise $10$ to the power of $1$ .

$\sqrt{10^{1} \cdot 10^{3}}$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{10^{1 + 3}}$

Step 2.2

Add $1$ and $3$ .

$\sqrt{10^{4}}$

Step 3

Raise $10$ to the power of $4$ .

$\sqrt{10000}$

Step 4

Rewrite $10000$ as $100^{2}$ .

$\sqrt{100^{2}}$

Step 5

Pull terms out from under the radical.

$| 100 |$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $100$ is $100$ .

$100$