Simplify square root of 16a- square root of 49a+ square root of 81a

$\sqrt{16 a} - \sqrt{49 a} + \sqrt{81 a}$

Step 1

Simplify each term.

Rewrite $16 a$ as ${(2^{2})}^{2} a$ .

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} a} - \sqrt{49 a} + \sqrt{81 a}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{{(2^{2})}^{2} a} - \sqrt{49 a} + \sqrt{81 a}$

Pull terms out from under the radical.

$2^{2} \sqrt{a} - \sqrt{49 a} + \sqrt{81 a}$

Raise $2$ to the power of $2$ .

$4 \sqrt{a} - \sqrt{49 a} + \sqrt{81 a}$

Rewrite $49$ as $7^{2}$ .

$4 \sqrt{a} - \sqrt{7^{2} a} + \sqrt{81 a}$

Pull terms out from under the radical.

$4 \sqrt{a} - (7 \sqrt{a}) + \sqrt{81 a}$

Multiply $7$ by $- 1$ .

$4 \sqrt{a} - 7 \sqrt{a} + \sqrt{81 a}$

Rewrite $81 a$ as ${(3^{2})}^{2} a$ .

Rewrite $81$ as $9^{2}$ .

$4 \sqrt{a} - 7 \sqrt{a} + \sqrt{9^{2} a}$

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

$4 \sqrt{a} - 7 \sqrt{a} + \sqrt{{(3^{2})}^{2} a}$

Pull terms out from under the radical.

$4 \sqrt{a} - 7 \sqrt{a} + 3^{2} \sqrt{a}$

Raise $3$ to the power of $2$ .

$4 \sqrt{a} - 7 \sqrt{a} + 9 \sqrt{a}$

Step 2

Simplify by adding terms.

Subtract $7 \sqrt{a}$ from $4 \sqrt{a}$ .

$- 3 \sqrt{a} + 9 \sqrt{a}$

Add $- 3 \sqrt{a}$ and $9 \sqrt{a}$ .

$6 \sqrt{a}$