Algebra Examples

$\frac{\sqrt{44} \cdot \sqrt{63}}{\sqrt{99}}$

Step 1

Combine $\sqrt{44}$ and $\sqrt{99}$ into a single radical.

$\sqrt{\frac{44}{99}} \cdot \sqrt{63}$

Step 2

Combine using the product rule for radicals.

$\sqrt{\frac{44}{99} \cdot 63}$

Step 3

Combine $\frac{44}{99}$ and $63$ .

$\sqrt{\frac{44 \cdot 63}{99}}$

Step 4

Reduce the expression $\frac{44 \cdot 63}{99}$ by cancelling the common factors.

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Step 4.1

Factor $11$ out of $44 \cdot 63$ .

$\sqrt{\frac{11 (4 \cdot 63)}{99}}$

Step 4.2

Factor $11$ out of $99$ .

$\sqrt{\frac{11 (4 \cdot 63)}{11 (9)}}$

Step 4.3

Cancel the common factor.

$\sqrt{\frac{11 (4 \cdot 63)}{11 \cdot 9}}$

Step 4.4

Rewrite the expression.

$\sqrt{\frac{4 \cdot 63}{9}}$

Step 5

Cancel the common factor of $63$ and $9$ .

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Step 5.1

Factor $9$ out of $4 \cdot 63$ .

$\sqrt{\frac{9 (4 \cdot 7)}{9}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $9$ out of $9$ .

$\sqrt{\frac{9 (4 \cdot 7)}{9 (1)}}$

Step 5.2.2

Cancel the common factor.

$\sqrt{\frac{9 (4 \cdot 7)}{9 \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$\sqrt{\frac{4 \cdot 7}{1}}$

Step 5.2.4

Divide $4 \cdot 7$ by $1$ .

$\sqrt{4 \cdot 7}$

Step 6

Multiply $4$ by $7$ .

$\sqrt{28}$

Step 7

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 7.1

Factor $4$ out of $28$ .

$\sqrt{4 (7)}$

Step 7.2

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

$\sqrt{2^{2} \cdot 7}$

Step 8

Pull terms out from under the radical.

$2 \sqrt{7}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{7}$

Decimal Form:

$5.29150262 \dots$