Basic Math Examples

$16^{2} + 30^{2} = \sqrt{c}$

Step 1

Rewrite the equation as $\sqrt{c} = 16^{2} + 30^{2}$ .

$\sqrt{c} = 16^{2} + 30^{2}$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{c}}^{2} = {(16^{2} + 30^{2})}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

${(c^{\frac{1}{2}})}^{2} = {(16^{2} + 30^{2})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(c^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${(c^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

$c^{\frac{1}{2} \cdot 2} = {(16^{2} + 30^{2})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$c^{\frac{1}{2} \cdot 2} = {(16^{2} + 30^{2})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$c^{1} = {(16^{2} + 30^{2})}^{2}$

Step 3.2.1.2

Simplify.

$c = {(16^{2} + 30^{2})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(16^{2} + 30^{2})}^{2}$ .

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Step 3.3.1.1

Simplify each term.

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Step 3.3.1.1.1

Raise $16$ to the power of $2$ .

$c = {(256 + 30^{2})}^{2}$

Step 3.3.1.1.2

Raise $30$ to the power of $2$ .

$c = {(256 + 900)}^{2}$

Step 3.3.1.2

Simplify the expression.

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Step 3.3.1.2.1

Add $256$ and $900$ .

$c = 1156^{2}$

Step 3.3.1.2.2

Raise $1156$ to the power of $2$ .

$c = 1336336$