Pre-Algebra Examples

$d = \sqrt{\frac{3 (180)}{2}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{3 (180)}{2}$ by cancelling the common factors.

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Step 1.1.1

Factor $2$ out of $3 (180)$ .

$d = \sqrt{\frac{2 (3 \cdot (90))}{2}}$

Step 1.1.2

Factor $2$ out of $2$ .

$d = \sqrt{\frac{2 (3 \cdot (90))}{2 (1)}}$

Step 1.1.3

Cancel the common factor.

$d = \sqrt{\frac{2 (3 \cdot (90))}{2 \cdot 1}}$

Step 1.1.4

Rewrite the expression.

$d = \sqrt{\frac{3 \cdot (90)}{1}}$

Step 1.2

Divide $3 \cdot (90)$ by $1$ .

$d = \sqrt{3 \cdot (90)}$

Step 2

Multiply $3$ by $90$ .

$d = \sqrt{270}$

Step 3

Rewrite $270$ as $3^{2} \cdot 30$ .

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Step 3.1

Factor $9$ out of $270$ .

$d = \sqrt{9 (30)}$

Step 3.2

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

$d = \sqrt{3^{2} \cdot 30}$

Step 4

Pull terms out from under the radical.

$d = 3 \sqrt{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = 3 \sqrt{30}$

Decimal Form:

$d = 16.43167672 \dots$