Algebra Examples

$\sqrt{5} \cdot \sqrt{5} \cdot \sqrt{2} \cdot \sqrt{2}$

Step 1

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5} \cdot \sqrt{2} \cdot \sqrt{2}$

Step 2

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5 \cdot 2} \cdot \sqrt{2}$

Step 3

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5 \cdot 2 \cdot 2}$

Step 4

Write the expression using exponents.

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Step 4.1

Multiply $5$ by $5$ .

$\sqrt{25 \cdot 2 \cdot 2}$

Step 4.2

Multiply.

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Step 4.2.1

Multiply $25$ by $2$ .

$\sqrt{50 \cdot 2}$

Step 4.2.2

Multiply $50$ by $2$ .

$\sqrt{100}$

Step 4.3

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

$\sqrt{10^{2}}$

Step 4.4

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

$10$