Finite Math Examples

$\sqrt{7} (6 \sqrt{2} - \sqrt{7})$

Step 1

Apply the distributive property.

$\sqrt{7} (6 \sqrt{2}) + \sqrt{7} (- \sqrt{7})$

Step 2

Multiply $\sqrt{7} (6 \sqrt{2})$ .

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Step 2.1

Combine using the product rule for radicals.

$6 \sqrt{7 \cdot 2} + \sqrt{7} (- \sqrt{7})$

Step 2.2

Multiply $7$ by $2$ .

$6 \sqrt{14} + \sqrt{7} (- \sqrt{7})$

Step 3

Multiply $\sqrt{7} (- \sqrt{7})$ .

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Step 3.1

Raise $\sqrt{7}$ to the power of $1$ .

$6 \sqrt{14} - ({\sqrt{7}}^{1} \sqrt{7})$

Step 3.2

Raise $\sqrt{7}$ to the power of $1$ .

$6 \sqrt{14} - ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

Step 3.3

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

$6 \sqrt{14} - {\sqrt{7}}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$6 \sqrt{14} - {\sqrt{7}}^{2}$

Step 4

Simplify each term.

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Step 4.1

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$6 \sqrt{14} - {(7^{\frac{1}{2}})}^{2}$

Step 4.1.2

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

$6 \sqrt{14} - 7^{\frac{1}{2} \cdot 2}$

Step 4.1.3

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

$6 \sqrt{14} - 7^{\frac{2}{2}}$

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

$6 \sqrt{14} - 7^{\frac{2}{2}}$

Step 4.1.4.2

Rewrite the expression.

$6 \sqrt{14} - 7^{1}$

Step 4.1.5

Evaluate the exponent.

$6 \sqrt{14} - 1 \cdot 7$

Step 4.2

Multiply $- 1$ by $7$ .

$6 \sqrt{14} - 7$

Step 5

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{14} - 7$

Decimal Form:

$15.44994432 \dots$