Finite Math Examples

$(\sqrt{4} + \sqrt{5}) (\sqrt{4 - \sqrt{5}})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $4$ as $2^{2}$ .

$(\sqrt{2^{2}} + \sqrt{5}) \sqrt{4 - \sqrt{5}}$

Step 1.1.2

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

$(2 + \sqrt{5}) \sqrt{4 - \sqrt{5}}$

Step 1.2

Simplify terms.

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Step 1.2.1

Apply the distributive property.

$2 \sqrt{4 - \sqrt{5}} + \sqrt{5} \sqrt{4 - \sqrt{5}}$

Step 1.2.2

Combine using the product rule for radicals.

$2 \sqrt{4 - \sqrt{5}} + \sqrt{5 (4 - \sqrt{5})}$

Step 2

The expression is constant, which means it can be rewritten with a factor of $x^{0}$ . The degree is the largest exponent on the variable.

$0$