Simplify square root of 9( square root of a^3+ square root of 7)a^3

$\sqrt{9} (\sqrt{a^{3}} + \sqrt{7}) a^{3}$

Step 1

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}} (\sqrt{a^{3}} + \sqrt{7}) a^{3}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$3 (\sqrt{a^{3}} + \sqrt{7}) a^{3}$

Step 3

Simplify each term.

Factor out $a^{2}$ .

$3 (\sqrt{a^{2} a} + \sqrt{7}) a^{3}$

Pull terms out from under the radical.

$3 (a \sqrt{a} + \sqrt{7}) a^{3}$

Step 4

Simplify by multiplying through.

Apply the distributive property.

$(3 (a \sqrt{a}) + 3 \sqrt{7}) a^{3}$

Apply the distributive property.

$3 a \sqrt{a} a^{3} + 3 \sqrt{7} a^{3}$

Step 5

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

Move $a^{3}$ .

$3 (a^{3} a) \sqrt{a} + 3 \sqrt{7} a^{3}$

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

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

$3 (a^{3} a^{1}) \sqrt{a} + 3 \sqrt{7} a^{3}$

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

$3 a^{3 + 1} \sqrt{a} + 3 \sqrt{7} a^{3}$

Add $3$ and $1$ .

$3 a^{4} \sqrt{a} + 3 \sqrt{7} a^{3}$