Algebra Examples

$3 \sqrt{5 a} \cdot 8 \sqrt{35 a^{2}}$

Step 1

Reorder $35$ and $a^{2}$ .

$3 \sqrt{5 a} \cdot (8 \sqrt{a^{2} \cdot 35})$

Step 2

Pull terms out from under the radical.

$3 \sqrt{5 a} \cdot (8 (a \sqrt{35}))$

Step 3

Multiply $3 \sqrt{5 a} (8 a \sqrt{35})$ .

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Step 3.1

Multiply $8$ by $3$ .

$24 \sqrt{5 a} (a \sqrt{35})$

Step 3.2

Combine using the product rule for radicals.

$24 (a \sqrt{5 a \cdot 35})$

Step 3.3

Multiply $35$ by $5$ .

$24 (a \sqrt{175 a})$

$24 (a \sqrt{175 a})$

Step 4

Rewrite $175 a$ as $5^{2} \cdot (7 a)$ .

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Step 4.1

Factor $25$ out of $175$ .

$24 (a \sqrt{25 (7) a})$

Step 4.2

Rewrite $25$ as $5^{2}$ .

$24 (a \sqrt{5^{2} \cdot 7 a})$

Step 4.3

Add parentheses.

$24 (a \sqrt{5^{2} \cdot (7 a)})$

$24 (a \sqrt{5^{2} \cdot (7 a)})$

Step 5

Pull terms out from under the radical.

$24 (a (5 \sqrt{7 a}))$

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

$24 (5 a \sqrt{7 a})$

Step 6.2

Multiply $5$ by $24$ .

$120 a \sqrt{7 a}$

$120 a \sqrt{7 a}$

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