Linear Algebra Examples

$\sqrt{18} \sqrt{\frac{45}{10}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{18 (\frac{45}{10})}$

Step 2

Combine $18$ and $\frac{45}{10}$ .

$\sqrt{\frac{18 \cdot 45}{10}}$

Step 3

Reduce the expression $\frac{18 \cdot 45}{10}$ by cancelling the common factors.

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Step 3.1

Factor $2$ out of $18 \cdot 45$ .

$\sqrt{\frac{2 (9 \cdot 45)}{10}}$

Step 3.2

Factor $2$ out of $10$ .

$\sqrt{\frac{2 (9 \cdot 45)}{2 (5)}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{2 (9 \cdot 45)}{2 \cdot 5}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{9 \cdot 45}{5}}$

Step 4

Cancel the common factor of $45$ and $5$ .

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Step 4.1

Factor $5$ out of $9 \cdot 45$ .

$\sqrt{\frac{5 (9 \cdot 9)}{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (9 \cdot 9)}{5 (1)}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{5 (9 \cdot 9)}{5 \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{9 \cdot 9}{1}}$

Step 4.2.4

Divide $9 \cdot 9$ by $1$ .

$\sqrt{9 \cdot 9}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $9$ by $9$ .

$\sqrt{81}$

Step 5.2

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2}}$

Step 5.3

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

$9$