Basic Math Examples

$\sqrt{24 a} \cdot \sqrt{32 b}$

Step 1

Rewrite $24 a$ as $2^{2} \cdot (6 a)$ .

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Step 1.1

Factor $4$ out of $24$ .

$\sqrt{4 (6) a} \cdot \sqrt{32 b}$

Step 1.2

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

$\sqrt{2^{2} \cdot 6 a} \cdot \sqrt{32 b}$

Step 1.3

Add parentheses.

$\sqrt{2^{2} \cdot (6 a)} \cdot \sqrt{32 b}$

$\sqrt{2^{2} \cdot (6 a)} \cdot \sqrt{32 b}$

Step 2

Pull terms out from under the radical.

$2 \sqrt{6 a} \cdot \sqrt{32 b}$

Step 3

Rewrite $32 b$ as ${(2^{2})}^{2} \cdot (2 b)$ .

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Step 3.1

Factor $16$ out of $32$ .

$2 \sqrt{6 a} \cdot \sqrt{16 (2) b}$

Step 3.2

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

$2 \sqrt{6 a} \cdot \sqrt{4^{2} \cdot 2 b}$

Step 3.3

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

$2 \sqrt{6 a} \cdot \sqrt{{(2^{2})}^{2} \cdot 2 b}$

Step 3.4

Add parentheses.

$2 \sqrt{6 a} \cdot \sqrt{{(2^{2})}^{2} \cdot (2 b)}$

$2 \sqrt{6 a} \cdot \sqrt{{(2^{2})}^{2} \cdot (2 b)}$

Step 4

Pull terms out from under the radical.

$2 \sqrt{6 a} \cdot (2^{2} \sqrt{2 b})$

Step 5

Multiply $2$ by $2^{2}$ by adding the exponents.

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Step 5.1

Move $2^{2}$ .

$2^{2} \cdot 2 \sqrt{6 a} \cdot \sqrt{2 b}$

Step 5.2

Multiply $2^{2}$ by $2$ .

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Step 5.2.1

Raise $2$ to the power of $1$ .

$2^{2} \cdot 2^{1} \sqrt{6 a} \cdot \sqrt{2 b}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 + 1} \sqrt{6 a} \cdot \sqrt{2 b}$

$2^{2 + 1} \sqrt{6 a} \cdot \sqrt{2 b}$

Step 5.3

Add $2$ and $1$ .

$2^{3} \sqrt{6 a} \cdot \sqrt{2 b}$

$2^{3} \sqrt{6 a} \cdot \sqrt{2 b}$

Step 6

Raise $2$ to the power of $3$ .

$8 \sqrt{6 a} \cdot \sqrt{2 b}$

Step 7

Multiply $8 \sqrt{6 a} \sqrt{2 b}$ .

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Step 7.1

Combine using the product rule for radicals.

$8 \sqrt{2 b (6 a)}$

Step 7.2

Multiply $6$ by $2$ .

$8 \sqrt{12 b a}$

$8 \sqrt{12 b a}$

Step 8

Rewrite $12 b a$ as $2^{2} \cdot (3 b a)$ .

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Step 8.1

Factor $4$ out of $12$ .

$8 \sqrt{4 (3) b a}$

Step 8.2

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

$8 \sqrt{2^{2} \cdot 3 b a}$

Step 8.3

Add parentheses.

$8 \sqrt{2^{2} \cdot 3 (b a)}$

Step 8.4

Add parentheses.

$8 \sqrt{2^{2} \cdot (3 b a)}$

$8 \sqrt{2^{2} \cdot (3 b a)}$

Step 9

Pull terms out from under the radical.

$8 (2 \sqrt{3 b a})$

Step 10

Multiply $2$ by $8$ .

$16 \sqrt{3 b a}$

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