Basic Math Examples

$4 \sqrt{2 a} \cdot (5 \sqrt{6 a y^{2}})$

Step 1

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

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Step 1.1

Move $a$ .

$4 \sqrt{2 a} \cdot (5 \sqrt{6 y^{2} a})$

Step 1.2

Reorder $6$ and $y^{2}$ .

$4 \sqrt{2 a} \cdot (5 \sqrt{y^{2} \cdot 6 a})$

Step 1.3

Add parentheses.

$4 \sqrt{2 a} \cdot (5 \sqrt{y^{2} \cdot (6 a)})$

$4 \sqrt{2 a} \cdot (5 \sqrt{y^{2} \cdot (6 a)})$

Step 2

Pull terms out from under the radical.

$4 \sqrt{2 a} \cdot (5 (y \sqrt{6 a}))$

Step 3

Multiply $4 \sqrt{2 a} (5 y \sqrt{6 a})$ .

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Step 3.1

Multiply $5$ by $4$ .

$20 \sqrt{2 a} (y \sqrt{6 a})$

Step 3.2

Combine using the product rule for radicals.

$20 (y \sqrt{2 a (6 a)})$

Step 3.3

Multiply $6$ by $2$ .

$20 (y \sqrt{12 a \cdot a})$

Step 3.4

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

$20 (y \sqrt{12 (a^{1} a)})$

Step 3.5

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

$20 (y \sqrt{12 (a^{1} a^{1})})$

Step 3.6

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

$20 (y \sqrt{12 a^{1 + 1}})$

Step 3.7

Add $1$ and $1$ .

$20 (y \sqrt{12 a^{2}})$

$20 (y \sqrt{12 a^{2}})$

Step 4

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

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Step 4.1

Factor $4$ out of $12$ .

$20 (y \sqrt{4 (3) a^{2}})$

Step 4.2

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

$20 (y \sqrt{2^{2} \cdot 3 a^{2}})$

Step 4.3

Move $3$ .

$20 (y \sqrt{2^{2} a^{2} \cdot 3})$

Step 4.4

Rewrite $2^{2} a^{2}$ as ${(2 a)}^{2}$ .

$20 (y \sqrt{{(2 a)}^{2} \cdot 3})$

$20 (y \sqrt{{(2 a)}^{2} \cdot 3})$

Step 5

Pull terms out from under the radical.

$20 (y (2 a \sqrt{3}))$

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

$20 (2 \sqrt{3} y a)$

Step 6.2

Multiply $2$ by $20$ .

$40 \sqrt{3} y a$

$40 \sqrt{3} y a$

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