Basic Math Examples

$4^{2} + b^{2} = {(\sqrt{69})}^{2}$

Step 1

Raise $4$ to the power of $2$ .

$16 + b^{2} = {\sqrt{69}}^{2}$

Step 2

Rewrite ${\sqrt{69}}^{2}$ as $69$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{69}$ as $69^{\frac{1}{2}}$ .

$16 + b^{2} = {(69^{\frac{1}{2}})}^{2}$

Step 2.2

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

$16 + b^{2} = 69^{\frac{1}{2} \cdot 2}$

Step 2.3

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

$16 + b^{2} = 69^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$16 + b^{2} = 69^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$16 + b^{2} = 69^{1}$

Step 2.5

Evaluate the exponent.

$16 + b^{2} = 69$

Step 3

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

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Step 3.1

Subtract $16$ from both sides of the equation.

$b^{2} = 69 - 16$

Step 3.2

Subtract $16$ from $69$ .

$b^{2} = 53$

Step 4

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

$b = \pm \sqrt{53}$

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.

$b = \sqrt{53}$

Step 5.2

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

$b = - \sqrt{53}$

Step 5.3

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

$b = \sqrt{53}, - \sqrt{53}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \sqrt{53}, - \sqrt{53}$

Decimal Form:

$b = 7.28010988 \dots, - 7.28010988 \dots$