Finite Math Examples

$24 = \sqrt{64 h + 10}$

Step 1

Rewrite the equation as $\sqrt{64 h + 10} = 24$ .

$\sqrt{64 h + 10} = 24$

Step 2

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

${\sqrt{64 h + 10}}^{2} = 24^{2}$

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 $\sqrt{64 h + 10}$ as ${(64 h + 10)}^{\frac{1}{2}}$ .

${({(64 h + 10)}^{\frac{1}{2}})}^{2} = 24^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(64 h + 10)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(64 h + 10)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(64 h + 10)}^{\frac{1}{2} \cdot 2} = 24^{2}$

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.

${(64 h + 10)}^{\frac{1}{2} \cdot 2} = 24^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(64 h + 10)}^{1} = 24^{2}$

Step 3.2.1.2

Simplify.

$64 h + 10 = 24^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $24$ to the power of $2$ .

$64 h + 10 = 576$

Step 4

Solve for $h$ .

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Step 4.1

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

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Step 4.1.1

Subtract $10$ from both sides of the equation.

$64 h = 576 - 10$

Step 4.1.2

Subtract $10$ from $576$ .

$64 h = 566$

Step 4.2

Divide each term in $64 h = 566$ by $64$ and simplify.

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Step 4.2.1

Divide each term in $64 h = 566$ by $64$ .

$\frac{64 h}{64} = \frac{566}{64}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $64$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{64 h}{64} = \frac{566}{64}$

Step 4.2.2.1.2

Divide $h$ by $1$ .

$h = \frac{566}{64}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $566$ and $64$ .

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Step 4.2.3.1.1

Factor $2$ out of $566$ .

$h = \frac{2 (283)}{64}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $2$ out of $64$ .

$h = \frac{2 \cdot 283}{2 \cdot 32}$

Step 4.2.3.1.2.2

Cancel the common factor.

$h = \frac{2 \cdot 283}{2 \cdot 32}$

Step 4.2.3.1.2.3

Rewrite the expression.

$h = \frac{283}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = \frac{283}{32}$

Decimal Form:

$h = 8.84375$

Mixed Number Form:

$h = 8 \frac{27}{32}$