Algebra Examples

3 \sqrt{2} (5 \sqrt{6} - 7 \sqrt{3})

$3 \sqrt{2} (5 \sqrt{6} - 7 \sqrt{3})$

Step 1

Apply the distributive property.

3 \sqrt{2} (5 \sqrt{6}) + 3 \sqrt{2} (- 7 \sqrt{3})

$3 \sqrt{2} (5 \sqrt{6}) + 3 \sqrt{2} (- 7 \sqrt{3})$

Step 2

Multiply

3 \sqrt{2} (5 \sqrt{6})

$3 \sqrt{2} (5 \sqrt{6})$ .

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Step 2.1

Multiply

5

$5$ by

3

$3$ .

15 \sqrt{2} \sqrt{6} + 3 \sqrt{2} (- 7 \sqrt{3})

$15 \sqrt{2} \sqrt{6} + 3 \sqrt{2} (- 7 \sqrt{3})$

Step 2.2

Combine using the product rule for radicals.

15 \sqrt{6 \cdot 2} + 3 \sqrt{2} (- 7 \sqrt{3})

$15 \sqrt{6 \cdot 2} + 3 \sqrt{2} (- 7 \sqrt{3})$

Step 2.3

Multiply

6

$6$ by

2

$2$ .

15 \sqrt{12} + 3 \sqrt{2} (- 7 \sqrt{3})

$15 \sqrt{12} + 3 \sqrt{2} (- 7 \sqrt{3})$

15 \sqrt{12} + 3 \sqrt{2} (- 7 \sqrt{3})

$15 \sqrt{12} + 3 \sqrt{2} (- 7 \sqrt{3})$

Step 3

Multiply

3 \sqrt{2} (- 7 \sqrt{3})

$3 \sqrt{2} (- 7 \sqrt{3})$ .

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Step 3.1

Multiply

- 7

$- 7$ by

3

$3$ .

15 \sqrt{12} - 21 \sqrt{2} \sqrt{3}

$15 \sqrt{12} - 21 \sqrt{2} \sqrt{3}$

Step 3.2

Combine using the product rule for radicals.

15 \sqrt{12} - 21 \sqrt{3 \cdot 2}

$15 \sqrt{12} - 21 \sqrt{3 \cdot 2}$

Step 3.3

Multiply

3

$3$ by

2

$2$ .

15 \sqrt{12} - 21 \sqrt{6}

$15 \sqrt{12} - 21 \sqrt{6}$

15 \sqrt{12} - 21 \sqrt{6}

$15 \sqrt{12} - 21 \sqrt{6}$

Step 4

Simplify each term.

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Step 4.1

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 4.1.1

Factor

4

$4$ out of

12

$12$ .

15 \sqrt{4 (3)} - 21 \sqrt{6}

$15 \sqrt{4 (3)} - 21 \sqrt{6}$

Step 4.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

15 \sqrt{2^{2} \cdot 3} - 21 \sqrt{6}

$15 \sqrt{2^{2} \cdot 3} - 21 \sqrt{6}$

15 \sqrt{2^{2} \cdot 3} - 21 \sqrt{6}

$15 \sqrt{2^{2} \cdot 3} - 21 \sqrt{6}$

Step 4.2

Pull terms out from under the radical.

15 (2 \sqrt{3}) - 21 \sqrt{6}

$15 (2 \sqrt{3}) - 21 \sqrt{6}$

Step 4.3

Multiply

2

$2$ by

15

$15$ .

30 \sqrt{3} - 21 \sqrt{6}

$30 \sqrt{3} - 21 \sqrt{6}$

30 \sqrt{3} - 21 \sqrt{6}

$30 \sqrt{3} - 21 \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

30 \sqrt{3} - 21 \sqrt{6}

$30 \sqrt{3} - 21 \sqrt{6}$

Decimal Form:

0.52223962 \dots

$0.52223962 \dots$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$