Algebra Examples

$\sqrt{48} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.1.1

Factor $16$ out of $48$ .

$\sqrt{16 (3)} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

Step 1.1.2

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

$\sqrt{4^{2} \cdot 3} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

Step 1.2

Pull terms out from under the radical.

$4 \sqrt{3} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

Step 1.3

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.3.1

Factor $9$ out of $27$ .

$4 \sqrt{3} + 3 \sqrt{9 (3)} - 7 (\sqrt{12} - \sqrt{75})$

Step 1.3.2

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

$4 \sqrt{3} + 3 \sqrt{3^{2} \cdot 3} - 7 (\sqrt{12} - \sqrt{75})$

Step 1.4

Pull terms out from under the radical.

$4 \sqrt{3} + 3 (3 \sqrt{3}) - 7 (\sqrt{12} - \sqrt{75})$

Step 1.5

Multiply $3$ by $3$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (\sqrt{12} - \sqrt{75})$

Step 1.6

Simplify each term.

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Step 1.6.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.6.1.1

Factor $4$ out of $12$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (\sqrt{4 (3)} - \sqrt{75})$

Step 1.6.1.2

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

$4 \sqrt{3} + 9 \sqrt{3} - 7 (\sqrt{2^{2} \cdot 3} - \sqrt{75})$

Step 1.6.2

Pull terms out from under the radical.

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - \sqrt{75})$

Step 1.6.3

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.6.3.1

Factor $25$ out of $75$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - \sqrt{25 (3)})$

Step 1.6.3.2

Rewrite $25$ as $5^{2}$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - \sqrt{5^{2} \cdot 3})$

Step 1.6.4

Pull terms out from under the radical.

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - (5 \sqrt{3}))$

Step 1.6.5

Multiply $5$ by $- 1$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - 5 \sqrt{3})$

Step 1.7

Subtract $5 \sqrt{3}$ from $2 \sqrt{3}$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (- 3 \sqrt{3})$

Step 1.8

Multiply $- 3$ by $- 7$ .

$4 \sqrt{3} + 9 \sqrt{3} + 21 \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $4 \sqrt{3}$ and $9 \sqrt{3}$ .

$13 \sqrt{3} + 21 \sqrt{3}$

Step 2.2

Add $13 \sqrt{3}$ and $21 \sqrt{3}$ .

$34 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$34 \sqrt{3}$

Decimal Form:

$58.88972745 \dots$