Simplify square root of 9a^2+ square root of 49b-a+ square root of b

$\sqrt{9 a^{2}} + \sqrt{49 b} - a + \sqrt{b}$

Step 1

Simplify each term.

Rewrite $9 a^{2}$ as ${(3 a)}^{2}$ .

$\sqrt{{(3 a)}^{2}} + \sqrt{49 b} - a + \sqrt{b}$

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

$3 a + \sqrt{49 b} - a + \sqrt{b}$

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

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

Pull terms out from under the radical.

$3 a + 7 \sqrt{b} - a + \sqrt{b}$

Step 2

Simplify by adding terms.

Subtract $a$ from $3 a$ .

$2 a + 7 \sqrt{b} + \sqrt{b}$

Add $7 \sqrt{b}$ and $\sqrt{b}$ .

$2 a + 8 \sqrt{b}$