Pre-Algebra Examples

$\sqrt{3} (3 - \sqrt{3}) + \sqrt[4]{3}$

Step 1

Apply the distributive property.

$\sqrt{3} \cdot 3 + \sqrt{3} (- \sqrt{3}) + \sqrt[4]{3}$

Step 2

Move $3$ to the left of $\sqrt{3}$ .

$3 \cdot \sqrt{3} + \sqrt{3} (- \sqrt{3}) + \sqrt[4]{3}$

Step 3

Multiply $\sqrt{3} (- \sqrt{3})$ .

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Step 3.1

Raise $\sqrt{3}$ to the power of $1$ .

$3 \cdot \sqrt{3} - ({\sqrt{3}}^{1} \sqrt{3}) + \sqrt[4]{3}$

Step 3.2

Raise $\sqrt{3}$ to the power of $1$ .

$3 \cdot \sqrt{3} - ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) + \sqrt[4]{3}$

Step 3.3

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

$3 \cdot \sqrt{3} - {\sqrt{3}}^{1 + 1} + \sqrt[4]{3}$

Step 3.4

Add $1$ and $1$ .

$3 \cdot \sqrt{3} - {\sqrt{3}}^{2} + \sqrt[4]{3}$

Step 4

Simplify each term.

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Step 4.1

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$3 \sqrt{3} - {(3^{\frac{1}{2}})}^{2} + \sqrt[4]{3}$

Step 4.1.2

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

$3 \sqrt{3} - 3^{\frac{1}{2} \cdot 2} + \sqrt[4]{3}$

Step 4.1.3

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

$3 \sqrt{3} - 3^{\frac{2}{2}} + \sqrt[4]{3}$

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

$3 \sqrt{3} - 3^{\frac{2}{2}} + \sqrt[4]{3}$

Step 4.1.4.2

Rewrite the expression.

$3 \sqrt{3} - 3^{1} + \sqrt[4]{3}$

Step 4.1.5

Evaluate the exponent.

$3 \sqrt{3} - 1 \cdot 3 + \sqrt[4]{3}$

Step 4.2

Multiply $- 1$ by $3$ .

$3 \sqrt{3} - 3 + \sqrt[4]{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3} - 3 + \sqrt[4]{3}$

Decimal Form:

$3.51222643 \dots$