Evaluate square root of 14-2 square root of 13* square root of 14+2 square root of 13

$\sqrt{14 - 2 \sqrt{13}} \cdot \sqrt{14 + 2 \sqrt{13}}$

Combine using the product rule for radicals.

$\sqrt{(14 - 2 \sqrt{13}) \cdot (14 + 2 \sqrt{13})}$

Expand $(14 - 2 \sqrt{13}) (14 + 2 \sqrt{13})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{14 (14 + 2 \sqrt{13}) - 2 \sqrt{13} (14 + 2 \sqrt{13})}$

Apply the distributive property.

$\sqrt{14 \cdot 14 + 14 (2 \sqrt{13}) - 2 \sqrt{13} (14 + 2 \sqrt{13})}$

Apply the distributive property.

$\sqrt{14 \cdot 14 + 14 (2 \sqrt{13}) - 2 \sqrt{13} \cdot 14 - 2 \sqrt{13} (2 \sqrt{13})}$

Simplify and combine like terms.

Simplify each term.

Multiply $14$ by $14$ .

$\sqrt{196 + 14 (2 \sqrt{13}) - 2 \sqrt{13} \cdot 14 - 2 \sqrt{13} (2 \sqrt{13})}$

Multiply $2$ by $14$ .

$\sqrt{196 + 28 \sqrt{13} - 2 \sqrt{13} \cdot 14 - 2 \sqrt{13} (2 \sqrt{13})}$

Multiply $14$ by $- 2$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 2 \sqrt{13} (2 \sqrt{13})}$

Multiply $- 2 \sqrt{13} (2 \sqrt{13})$ .

Multiply $2$ by $- 2$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 \sqrt{13} \sqrt{13}}$

Raise $\sqrt{13}$ to the power of $1$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 ({\sqrt{13}}^{1} \sqrt{13})}$

Raise $\sqrt{13}$ to the power of $1$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 ({\sqrt{13}}^{1} {\sqrt{13}}^{1})}$

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

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 {\sqrt{13}}^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 {\sqrt{13}}^{2}}$

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 {(13^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 \cdot 13^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 \cdot 13^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 \cdot 13^{\frac{2}{2}}}$

Rewrite the expression.

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 \cdot 13^{1}}$

Evaluate the exponent.

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 4 \cdot 13}$

Multiply $- 4$ by $13$ .

$\sqrt{196 + 28 \sqrt{13} - 28 \sqrt{13} - 52}$

Subtract $52$ from $196$ .

$\sqrt{144 + 28 \sqrt{13} - 28 \sqrt{13}}$

Subtract $28 \sqrt{13}$ from $28 \sqrt{13}$ .

$\sqrt{144 + 0}$

Add $144$ and $0$ .

$\sqrt{144}$

Rewrite $144$ as $12^{2}$ .

$\sqrt{12^{2}}$

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

$12$

Evaluate square root of 14-2 square root of 13* square root of 14+2 square root of 13

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