Pre-Algebra Examples

$4 + b^{2} = {(8 \sqrt{3})}^{2}$

Step 1

Simplify ${(8 \sqrt{3})}^{2}$ .

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Step 1.1

Rewrite.

$4 + b^{2} = 0 + 0 + {(8 \sqrt{3})}^{2}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Apply the product rule to $8 \sqrt{3}$ .

$4 + b^{2} = 8^{2} {\sqrt{3}}^{2}$

Step 1.2.2

Raise $8$ to the power of $2$ .

$4 + b^{2} = 64 {\sqrt{3}}^{2}$

Step 1.3

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

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Step 1.3.1

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

$4 + b^{2} = 64 {(3^{\frac{1}{2}})}^{2}$

Step 1.3.2

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

$4 + b^{2} = 64 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 1.3.3

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

$4 + b^{2} = 64 \cdot 3^{\frac{2}{2}}$

Step 1.3.4

Cancel the common factor of $2$ .

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Step 1.3.4.1

Cancel the common factor.

$4 + b^{2} = 64 \cdot 3^{\frac{2}{2}}$

Step 1.3.4.2

Rewrite the expression.

$4 + b^{2} = 64 \cdot 3^{1}$

Step 1.3.5

Evaluate the exponent.

$4 + b^{2} = 64 \cdot 3$

Step 1.4

Multiply $64$ by $3$ .

$4 + b^{2} = 192$

Step 2

Move all terms not containing $b$ to the right side of the equation.

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Step 2.1

Subtract $4$ from both sides of the equation.

$b^{2} = 192 - 4$

Step 2.2

Subtract $4$ from $192$ .

$b^{2} = 188$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$b = \pm \sqrt{188}$

Step 4

Simplify $\pm \sqrt{188}$ .

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Step 4.1

Rewrite $188$ as $2^{2} \cdot 47$ .

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Step 4.1.1

Factor $4$ out of $188$ .

$b = \pm \sqrt{4 (47)}$

Step 4.1.2

Rewrite $4$ as $2^{2}$ .

$b = \pm \sqrt{2^{2} \cdot 47}$

Step 4.2

Pull terms out from under the radical.

$b = \pm 2 \sqrt{47}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$b = 2 \sqrt{47}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$b = - 2 \sqrt{47}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$b = 2 \sqrt{47}, - 2 \sqrt{47}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = 2 \sqrt{47}, - 2 \sqrt{47}$

Decimal Form:

$b = 13.71130920 \dots, - 13.71130920 \dots$