Finite Math Examples

$\sqrt{u - 10 - 2} = 4$

Step 1

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

${\sqrt{u - 10 - 2}}^{2} = 4^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{u - 10 - 2}$ as ${(u - 10 - 2)}^{\frac{1}{2}}$ .

${({(u - 10 - 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(u - 10 - 2)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(u - 10 - 2)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(u - 10 - 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(u - 10 - 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(u - 10 - 2)}^{1} = 4^{2}$

Step 2.2.1.2

Subtract $2$ from $- 10$ .

${(u - 12)}^{1} = 4^{2}$

Step 2.2.1.3

Simplify.

$u - 12 = 4^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$u - 12 = 16$

Step 3

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

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Step 3.1

Add $12$ to both sides of the equation.

$u = 16 + 12$

Step 3.2

Add $16$ and $12$ .

$u = 28$