Pre-Algebra Examples

${(4 - \sqrt{6})}^{2}$

Step 1

Rewrite ${(4 - \sqrt{6})}^{2}$ as $(4 - \sqrt{6}) (4 - \sqrt{6})$ .

$(4 - \sqrt{6}) (4 - \sqrt{6})$

Step 2

Expand $(4 - \sqrt{6}) (4 - \sqrt{6})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$4 (4 - \sqrt{6}) - \sqrt{6} (4 - \sqrt{6})$

Step 2.2

Apply the distributive property.

$4 \cdot 4 + 4 (- \sqrt{6}) - \sqrt{6} (4 - \sqrt{6})$

Step 2.3

Apply the distributive property.

$4 \cdot 4 + 4 (- \sqrt{6}) - \sqrt{6} \cdot 4 - \sqrt{6} (- \sqrt{6})$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $4$ by $4$ .

$16 + 4 (- \sqrt{6}) - \sqrt{6} \cdot 4 - \sqrt{6} (- \sqrt{6})$

Step 3.1.2

Multiply $- 1$ by $4$ .

$16 - 4 \sqrt{6} - \sqrt{6} \cdot 4 - \sqrt{6} (- \sqrt{6})$

Step 3.1.3

Multiply $4$ by $- 1$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} - \sqrt{6} (- \sqrt{6})$

Step 3.1.4

Multiply $- \sqrt{6} (- \sqrt{6})$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} + 1 \sqrt{6} \sqrt{6}$

Step 3.1.4.2

Multiply $\sqrt{6}$ by $1$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} + \sqrt{6} \sqrt{6}$

Step 3.1.4.3

Raise $\sqrt{6}$ to the power of $1$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{1} \sqrt{6}$

Step 3.1.4.4

Raise $\sqrt{6}$ to the power of $1$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{1} {\sqrt{6}}^{1}$

Step 3.1.4.5

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

$16 - 4 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{1 + 1}$

Step 3.1.4.6

Add $1$ and $1$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} + {\sqrt{6}}^{2}$

Step 3.1.5

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Step 3.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$16 - 4 \sqrt{6} - 4 \sqrt{6} + {(6^{\frac{1}{2}})}^{2}$

Step 3.1.5.2

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

$16 - 4 \sqrt{6} - 4 \sqrt{6} + 6^{\frac{1}{2} \cdot 2}$

Step 3.1.5.3

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

$16 - 4 \sqrt{6} - 4 \sqrt{6} + 6^{\frac{2}{2}}$

Step 3.1.5.4

Cancel the common factor of $2$ .

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Step 3.1.5.4.1

Cancel the common factor.

$16 - 4 \sqrt{6} - 4 \sqrt{6} + 6^{\frac{2}{2}}$

Step 3.1.5.4.2

Rewrite the expression.

$16 - 4 \sqrt{6} - 4 \sqrt{6} + 6^{1}$

Step 3.1.5.5

Evaluate the exponent.

$16 - 4 \sqrt{6} - 4 \sqrt{6} + 6$

Step 3.2

Add $16$ and $6$ .

$22 - 4 \sqrt{6} - 4 \sqrt{6}$

Step 3.3

Subtract $4 \sqrt{6}$ from $- 4 \sqrt{6}$ .

$22 - 8 \sqrt{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$22 - 8 \sqrt{6}$

Decimal Form:

$2.40408205 \dots$