Algebra Examples

$\sqrt{2 a \cdot \sqrt{14 a^{3}} \cdot \sqrt{5 a}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{2 a \cdot \sqrt{5 a (14 a^{3})}}$

Step 2

Multiply $14$ by $5$ .

$\sqrt{2 a \cdot \sqrt{70 a \cdot a^{3}}}$

Step 3

Multiply $a$ by $a^{3}$ by adding the exponents.

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Step 3.1

Move $a^{3}$ .

$\sqrt{2 a \cdot \sqrt{70 (a^{3} a)}}$

Step 3.2

Multiply $a^{3}$ by $a$ .

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Step 3.2.1

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

$\sqrt{2 a \cdot \sqrt{70 (a^{3} a^{1})}}$

Step 3.2.2

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

$\sqrt{2 a \cdot \sqrt{70 a^{3 + 1}}}$

Step 3.3

Add $3$ and $1$ .

$\sqrt{2 a \cdot \sqrt{70 a^{4}}}$

Step 4

Rewrite $70 a^{4}$ as ${(a^{2})}^{2} \cdot 70$ .

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Step 4.1

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{2 a \sqrt{70 {(a^{2})}^{2}}}$

Step 4.2

Reorder $70$ and ${(a^{2})}^{2}$ .

$\sqrt{2 a \sqrt{{(a^{2})}^{2} \cdot 70}}$

Step 5

Pull terms out from under the radical.

$\sqrt{2 a \cdot a^{2} \sqrt{70}}$

Step 6

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

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Step 6.1

Move $a^{2}$ .

$\sqrt{2 (a^{2} a) \sqrt{70}}$

Step 6.2

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

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Step 6.2.1

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

$\sqrt{2 (a^{2} a^{1}) \sqrt{70}}$

Step 6.2.2

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

$\sqrt{2 a^{2 + 1} \sqrt{70}}$

Step 6.3

Add $2$ and $1$ .

$\sqrt{2 a^{3} \sqrt{70}}$

Step 7

Rewrite $2 a^{3} \sqrt{70}$ as $a^{2} \cdot (2 a \sqrt{70})$ .

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Step 7.1

Factor out $a^{2}$ .

$\sqrt{2 (a^{2} a) \sqrt{70}}$

Step 7.2

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

$\sqrt{a^{2} \cdot 2 a \sqrt{70}}$

Step 7.3

Add parentheses.

$\sqrt{a^{2} \cdot 2 (a \sqrt{70})}$

Step 7.4

Add parentheses.

$\sqrt{a^{2} \cdot (2 a \sqrt{70})}$

Step 8

Pull terms out from under the radical.

$a \sqrt{2 a \sqrt{70}}$