Simplify square root of 2a* square root of 14a^3* square root of 5a

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

Combine using the product rule for radicals.

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

Multiply $14$ by $5$ .

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

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

Move $a^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

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

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

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

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

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

Pull terms out from under the radical.

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

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Factor out $a^{2}$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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