Basic Math Examples

$\sqrt{7} (9 - \sqrt{7}) + 9 \sqrt{7}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\sqrt{7} \cdot 9 + \sqrt{7} (- \sqrt{7}) + 9 \sqrt{7}$

Step 1.2

Move $9$ to the left of $\sqrt{7}$ .

$9 \cdot \sqrt{7} + \sqrt{7} (- \sqrt{7}) + 9 \sqrt{7}$

Step 1.3

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

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Step 1.3.1

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

$9 \cdot \sqrt{7} - ({\sqrt{7}}^{1} \sqrt{7}) + 9 \sqrt{7}$

Step 1.3.2

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

$9 \cdot \sqrt{7} - ({\sqrt{7}}^{1} {\sqrt{7}}^{1}) + 9 \sqrt{7}$

Step 1.3.3

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

$9 \cdot \sqrt{7} - {\sqrt{7}}^{1 + 1} + 9 \sqrt{7}$

Step 1.3.4

Add $1$ and $1$ .

$9 \cdot \sqrt{7} - {\sqrt{7}}^{2} + 9 \sqrt{7}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

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

$9 \sqrt{7} - {(7^{\frac{1}{2}})}^{2} + 9 \sqrt{7}$

Step 1.4.1.2

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

$9 \sqrt{7} - 7^{\frac{1}{2} \cdot 2} + 9 \sqrt{7}$

Step 1.4.1.3

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

$9 \sqrt{7} - 7^{\frac{2}{2}} + 9 \sqrt{7}$

Step 1.4.1.4

Cancel the common factor of $2$ .

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Step 1.4.1.4.1

Cancel the common factor.

$9 \sqrt{7} - 7^{\frac{2}{2}} + 9 \sqrt{7}$

Step 1.4.1.4.2

Rewrite the expression.

$9 \sqrt{7} - 7^{1} + 9 \sqrt{7}$

Step 1.4.1.5

Evaluate the exponent.

$9 \sqrt{7} - 1 \cdot 7 + 9 \sqrt{7}$

Step 1.4.2

Multiply $- 1$ by $7$ .

$9 \sqrt{7} - 7 + 9 \sqrt{7}$

Step 2

Add $9 \sqrt{7}$ and $9 \sqrt{7}$ .

$- 7 + 18 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 7 + 18 \sqrt{7}$

Decimal Form:

$40.62352359 \dots$