Basic Math Examples

3 \sqrt{8} \cdot 3 \sqrt{10}

$3 \sqrt{8} \cdot 3 \sqrt{10}$

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

$8$ .

3 \sqrt{4 (2)} \cdot (3 \sqrt{10})

$3 \sqrt{4 (2)} \cdot (3 \sqrt{10})$

Step 1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

3 \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{10})

$3 \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{10})$

3 \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{10})

$3 \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{10})$

Step 2

Pull terms out from under the radical.

3 (2 \sqrt{2}) \cdot (3 \sqrt{10})

$3 (2 \sqrt{2}) \cdot (3 \sqrt{10})$

Step 3

Multiply

2

$2$ by

3

$3$ .

6 \sqrt{2} \cdot (3 \sqrt{10})

$6 \sqrt{2} \cdot (3 \sqrt{10})$

Step 4

Multiply

6 \sqrt{2} (3 \sqrt{10})

$6 \sqrt{2} (3 \sqrt{10})$ .

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Step 4.1

Multiply

3

$3$ by

6

$6$ .

18 \sqrt{2} \sqrt{10}

$18 \sqrt{2} \sqrt{10}$

Step 4.2

Combine using the product rule for radicals.

18 \sqrt{10 \cdot 2}

$18 \sqrt{10 \cdot 2}$

Step 4.3

Multiply

10

$10$ by

2

$2$ .

18 \sqrt{20}

$18 \sqrt{20}$

18 \sqrt{20}

$18 \sqrt{20}$

Step 5

Rewrite

20

$20$ as

2^{2} \cdot 5

$2^{2} \cdot 5$ .

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Step 5.1

Factor

4

$4$ out of

20

$20$ .

18 \sqrt{4 (5)}

$18 \sqrt{4 (5)}$

Step 5.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

18 \sqrt{2^{2} \cdot 5}

$18 \sqrt{2^{2} \cdot 5}$

18 \sqrt{2^{2} \cdot 5}

$18 \sqrt{2^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

18 (2 \sqrt{5})

$18 (2 \sqrt{5})$

Step 7

Multiply

2

$2$ by

18

$18$ .

36 \sqrt{5}

$36 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

36 \sqrt{5}

$36 \sqrt{5}$

Decimal Form:

80.49844718 \dots

$80.49844718 \dots$

3 \sqrt[]{8} \cdot 3 \sqrt[]{10}

$3 \sqrt[]{8} \cdot 3 \sqrt[]{10}$

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

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