Basic Math Examples

$\sqrt{1 - (\frac{7}{64} + \frac{6}{8})}$

Step 1

Cancel the common factor of $6$ and $8$ .

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Step 1.1

Factor $2$ out of $6$ .

$\sqrt{1 - (\frac{7}{64} + \frac{2 (3)}{8})}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $8$ .

$\sqrt{1 - (\frac{7}{64} + \frac{2 \cdot 3}{2 \cdot 4})}$

Step 1.2.2

Cancel the common factor.

$\sqrt{1 - (\frac{7}{64} + \frac{2 \cdot 3}{2 \cdot 4})}$

Step 1.2.3

Rewrite the expression.

$\sqrt{1 - (\frac{7}{64} + \frac{3}{4})}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\sqrt{1 - (\frac{7}{64} + \frac{3}{4} \cdot \frac{16}{16})}$

Step 3

Write each expression with a common denominator of $64$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{4}$ by $\frac{16}{16}$ .

$\sqrt{1 - (\frac{7}{64} + \frac{3 \cdot 16}{4 \cdot 16})}$

Step 3.2

Multiply $4$ by $16$ .

$\sqrt{1 - (\frac{7}{64} + \frac{3 \cdot 16}{64})}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{1 - \frac{7 + 3 \cdot 16}{64}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $16$ .

$\sqrt{1 - \frac{7 + 48}{64}}$

Step 5.2

Add $7$ and $48$ .

$\sqrt{1 - \frac{55}{64}}$

Step 6

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{64}{64} - \frac{55}{64}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{64 - 55}{64}}$

Step 8

Subtract $55$ from $64$ .

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

Step 9

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

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

Step 10

Simplify the numerator.

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Step 10.1

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

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

Step 10.2

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

$\frac{3}{\sqrt{64}}$

Step 11

Simplify the denominator.

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Step 11.1

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

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

Step 11.2

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

$\frac{3}{8}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{8}$

Decimal Form:

$0.375$