Basic Math Examples

4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{8}})

$4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{8}})$

Step 1

Rewrite

8

$8$ as

2^{2} \cdot 2

$2^{2} \cdot 2$ .

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Step 1.1

Factor

4

$4$ out of

8

$8$ .

4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{4 (2)}})

$4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{4 (2)}})$

Step 1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{2^{2} \cdot 2}})

$4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{2^{2} \cdot 2}})$

4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{2^{2} \cdot 2}})

$4 \sqrt{2} (5 \sqrt{6 - 3 \sqrt{2^{2} \cdot 2}})$

Step 2

Pull terms out from under the radical.

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

$4 \sqrt{2} (5 \sqrt{6 - 3 (2 \sqrt{2})})$

Step 3

Multiply

2

$2$ by

- 3

$- 3$ .

4 \sqrt{2} (5 \sqrt{6 - 6 \sqrt{2}})

$4 \sqrt{2} (5 \sqrt{6 - 6 \sqrt{2}})$

Step 4

Multiply

4 \sqrt{2} (5 \sqrt{6 - 6 \sqrt{2}})

$4 \sqrt{2} (5 \sqrt{6 - 6 \sqrt{2}})$ .

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Step 4.1

Multiply

5

$5$ by

4

$4$ .

20 \sqrt{2} \sqrt{6 - 6 \sqrt{2}}

$20 \sqrt{2} \sqrt{6 - 6 \sqrt{2}}$

Step 4.2

Combine using the product rule for radicals.

20 \sqrt{(6 - 6 \sqrt{2}) \cdot 2}

$20 \sqrt{(6 - 6 \sqrt{2}) \cdot 2}$

20 \sqrt{(6 - 6 \sqrt{2}) \cdot 2}

$20 \sqrt{(6 - 6 \sqrt{2}) \cdot 2}$