Algebra Examples

$\frac{- \sqrt{36}}{\sqrt{64}}$

Step 1

Combine $\sqrt{36}$ and $\sqrt{64}$ into a single radical.

$- \sqrt{\frac{36}{64}}$

Step 2

Cancel the common factor of $36$ and $64$ .

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Step 2.1

Factor $4$ out of $36$ .

$- \sqrt{\frac{4 (9)}{64}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $64$ .

$- \sqrt{\frac{4 \cdot 9}{4 \cdot 16}}$

Step 2.2.2

Cancel the common factor.

$- \sqrt{\frac{4 \cdot 9}{4 \cdot 16}}$

Step 2.2.3

Rewrite the expression.

$- \sqrt{\frac{9}{16}}$

Step 3

Rewrite $\sqrt{\frac{9}{16}}$ as $\frac{\sqrt{9}}{\sqrt{16}}$ .

$- \frac{\sqrt{9}}{\sqrt{16}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$- \frac{\sqrt{3^{2}}}{\sqrt{16}}$

Step 4.2

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

$- \frac{3}{\sqrt{16}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $16$ as $4^{2}$ .

$- \frac{3}{\sqrt{4^{2}}}$

Step 5.2

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

$- \frac{3}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{4}$

Decimal Form:

$- 0.75$