Trigonometry Examples

$\sqrt{\frac{18}{25} \cdot \frac{25}{32}}$

Step 1

Multiply $\frac{18}{25}$ by $\frac{25}{32}$ .

$\sqrt{\frac{18 \cdot 25}{25 \cdot 32}}$

Step 2

Reduce the expression $\frac{18 \cdot 25}{25 \cdot 32}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $18 \cdot 25$ .

$\sqrt{\frac{2 (9 \cdot 25)}{25 \cdot 32}}$

Step 2.2

Factor $2$ out of $25 \cdot 32$ .

$\sqrt{\frac{2 (9 \cdot 25)}{2 (25 \cdot 16)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 (9 \cdot 25)}{2 (25 \cdot 16)}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{9 \cdot 25}{25 \cdot 16}}$

Step 3

Cancel the common factor of $25$ .

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{9 \cdot 25}{25 \cdot 16}}$

Step 3.2

Rewrite the expression.

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

Step 4

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

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

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Simplify the denominator.

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Step 6.1

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

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

Step 6.2

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

$\frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$