Algebra Examples

$\frac{(\sqrt{63} + \sqrt{112}) \cdot \sqrt{28}}{42}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 1.1.1

Factor $9$ out of $63$ .

$\frac{(\sqrt{9 (7)} + \sqrt{112}) \sqrt{28}}{42}$

Step 1.1.2

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

$\frac{(\sqrt{3^{2} \cdot 7} + \sqrt{112}) \sqrt{28}}{42}$

Step 1.2

Pull terms out from under the radical.

$\frac{(3 \sqrt{7} + \sqrt{112}) \sqrt{28}}{42}$

Step 1.3

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 1.3.1

Factor $16$ out of $112$ .

$\frac{(3 \sqrt{7} + \sqrt{16 (7)}) \sqrt{28}}{42}$

Step 1.3.2

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

$\frac{(3 \sqrt{7} + \sqrt{4^{2} \cdot 7}) \sqrt{28}}{42}$

Step 1.4

Pull terms out from under the radical.

$\frac{(3 \sqrt{7} + 4 \sqrt{7}) \sqrt{28}}{42}$

Step 1.5

Add $3 \sqrt{7}$ and $4 \sqrt{7}$ .

$\frac{7 \sqrt{7} \sqrt{28}}{42}$

Step 1.6

Combine exponents.

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Step 1.6.1

Combine using the product rule for radicals.

$\frac{7 \sqrt{28 \cdot 7}}{42}$

Step 1.6.2

Multiply $28$ by $7$ .

$\frac{7 \sqrt{196}}{42}$

Step 1.7

Rewrite $196$ as $14^{2}$ .

$\frac{7 \sqrt{14^{2}}}{42}$

Step 1.8

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

$\frac{7 \cdot 14}{42}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Multiply $7$ by $14$ .

$\frac{98}{42}$

Step 2.2

Cancel the common factor of $98$ and $42$ .

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Step 2.2.1

Factor $14$ out of $98$ .

$\frac{14 (7)}{42}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $14$ out of $42$ .

$\frac{14 \cdot 7}{14 \cdot 3}$

Step 2.2.2.2

Cancel the common factor.

$\frac{14 \cdot 7}{14 \cdot 3}$

Step 2.2.2.3

Rewrite the expression.

$\frac{7}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{3}$

Decimal Form:

$2.\overline{3}$

Mixed Number Form:

$2 \frac{1}{3}$