Simplify ( square root of x- square root of 13)^2

${(\sqrt{x} - \sqrt{13})}^{2}$

Step 1

Rewrite ${(\sqrt{x} - \sqrt{13})}^{2}$ as $(\sqrt{x} - \sqrt{13}) (\sqrt{x} - \sqrt{13})$ .

$(\sqrt{x} - \sqrt{13}) (\sqrt{x} - \sqrt{13})$

Step 2

Expand $(\sqrt{x} - \sqrt{13}) (\sqrt{x} - \sqrt{13})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{x} (\sqrt{x} - \sqrt{13}) - \sqrt{13} (\sqrt{x} - \sqrt{13})$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} (\sqrt{x} - \sqrt{13})$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $\sqrt{x} \sqrt{x}$ .

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

${\sqrt{x}}^{1} \sqrt{x} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

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

${\sqrt{x}}^{1} {\sqrt{x}}^{1} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

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

${\sqrt{x}}^{1 + 1} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Add $1$ and $1$ .

${\sqrt{x}}^{2} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

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

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

${(x^{\frac{1}{2}})}^{2} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

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

$x^{\frac{1}{2} \cdot 2} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

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

$x^{\frac{2}{2}} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{2}{2}} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Rewrite the expression.

$x^{1} + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Simplify.

$x + \sqrt{x} (- \sqrt{13}) - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Combine using the product rule for radicals.

$x - \sqrt{x \cdot 13} - \sqrt{13} \sqrt{x} - \sqrt{13} (- \sqrt{13})$

Combine using the product rule for radicals.

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} - \sqrt{13} (- \sqrt{13})$

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

Multiply $- 1$ by $- 1$ .

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + 1 \sqrt{13} \sqrt{13}$

Multiply $\sqrt{13}$ by $1$ .

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + \sqrt{13} \sqrt{13}$

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

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + {\sqrt{13}}^{1} \sqrt{13}$

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

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + {\sqrt{13}}^{1} {\sqrt{13}}^{1}$

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

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + {\sqrt{13}}^{1 + 1}$

Add $1$ and $1$ .

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + {\sqrt{13}}^{2}$

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

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

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + {(13^{\frac{1}{2}})}^{2}$

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

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + 13^{\frac{1}{2} \cdot 2}$

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

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + 13^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + 13^{\frac{2}{2}}$

Rewrite the expression.

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + 13^{1}$

Evaluate the exponent.

$x - \sqrt{x \cdot 13} - \sqrt{x \cdot 13} + 13$

Subtract $\sqrt{x \cdot 13}$ from $- \sqrt{x \cdot 13}$ .

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

Step 4

Reorder factors in $x - 2 \sqrt{x \cdot 13} + 13$ .

$x - 2 \sqrt{13 x} + 13$

Simplify ( square root of x- square root of 13)^2

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