Basic Math Examples

$2 - 9 \div \sqrt{\frac{9}{64}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$2 - \frac{9}{\sqrt{\frac{9}{64}}}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Rewrite $\sqrt{\frac{9}{64}}$ as $\frac{\sqrt{9}}{\sqrt{64}}$ .

$2 - \frac{9}{\frac{\sqrt{9}}{\sqrt{64}}}$

Step 1.2.2

Simplify the numerator.

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Step 1.2.2.1

Rewrite $9$ as $3^{2}$ .

$2 - \frac{9}{\frac{\sqrt{3^{2}}}{\sqrt{64}}}$

Step 1.2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$2 - \frac{9}{\frac{3}{\sqrt{64}}}$

Step 1.2.3

Simplify the denominator.

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Step 1.2.3.1

Rewrite $64$ as $8^{2}$ .

$2 - \frac{9}{\frac{3}{\sqrt{8^{2}}}}$

Step 1.2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$2 - \frac{9}{\frac{3}{8}}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$2 - (9 (\frac{8}{3}))$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $9$ .

$2 - (3 (3) \frac{8}{3})$

Step 1.4.2

Cancel the common factor.

$2 - (3 \cdot 3 \frac{8}{3})$

Step 1.4.3

Rewrite the expression.

$2 - (3 \cdot 8)$

Step 1.5

Multiply $3$ by $8$ .

$2 - 1 \cdot 24$

Step 1.6

Multiply $- 1$ by $24$ .

$2 - 24$

Step 2

Subtract $24$ from $2$ .

$- 22$