Basic Math Examples

$\sqrt{98} \cdot 3 \sqrt{96}$

Step 1

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.1

Factor $49$ out of $98$ .

$\sqrt{49 (2)} \cdot (3 \sqrt{96})$

Step 1.2

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2} \cdot (3 \sqrt{96})$

$\sqrt{7^{2} \cdot 2} \cdot (3 \sqrt{96})$

Step 2

Pull terms out from under the radical.

$7 \sqrt{2} \cdot (3 \sqrt{96})$

Step 3

Rewrite $96$ as $4^{2} \cdot 6$ .

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Step 3.1

Factor $16$ out of $96$ .

$7 \sqrt{2} \cdot (3 \sqrt{16 (6)})$

Step 3.2

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

$7 \sqrt{2} \cdot (3 \sqrt{4^{2} \cdot 6})$

$7 \sqrt{2} \cdot (3 \sqrt{4^{2} \cdot 6})$

Step 4

Pull terms out from under the radical.

$7 \sqrt{2} \cdot (3 (4 \sqrt{6}))$

Step 5

Multiply $4$ by $3$ .

$7 \sqrt{2} \cdot (12 \sqrt{6})$

Step 6

Multiply $7 \sqrt{2} (12 \sqrt{6})$ .

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Step 6.1

Multiply $12$ by $7$ .

$84 \sqrt{2} \sqrt{6}$

Step 6.2

Combine using the product rule for radicals.

$84 \sqrt{6 \cdot 2}$

Step 6.3

Multiply $6$ by $2$ .

$84 \sqrt{12}$

$84 \sqrt{12}$

Step 7

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

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Step 7.1

Factor $4$ out of $12$ .

$84 \sqrt{4 (3)}$

Step 7.2

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

$84 \sqrt{2^{2} \cdot 3}$

$84 \sqrt{2^{2} \cdot 3}$

Step 8

Pull terms out from under the radical.

$84 (2 \sqrt{3})$

Step 9

Multiply $2$ by $84$ .

$168 \sqrt{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$168 \sqrt{3}$

Decimal Form:

$290.98453567 \dots$

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