Basic Math Examples

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

Step 1

Reorder $5$ and $a^{2}$ .

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

Step 2

Pull terms out from under the radical.

$a \sqrt{5} \cdot \sqrt{35 a}$

Step 3

Multiply $a \sqrt{5} \sqrt{35 a}$ .

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Step 3.1

Combine using the product rule for radicals.

$a \sqrt{35 a \cdot 5}$

Step 3.2

Multiply $5$ by $35$ .

$a \sqrt{175 a}$

Step 4

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

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Step 4.1

Factor $25$ out of $175$ .

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

Step 4.2

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

$a \sqrt{5^{2} \cdot 7 a}$

Step 4.3

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Step 6

Rewrite using the commutative property of multiplication.

$5 a \sqrt{7 a}$