Simplify 15+8 square root of 7+ square root of 112

$15 + 8 \sqrt{7} + \sqrt{112}$

Simplify each term.

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$15 + 8 \sqrt{7} + \sqrt{16 (7)}$

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

$15 + 8 \sqrt{7} + \sqrt{4^{2} \cdot 7}$

Pull terms out from under the radical.

$15 + 8 \sqrt{7} + 4 \sqrt{7}$

Add $8 \sqrt{7}$ and $4 \sqrt{7}$ .

$15 + 12 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$15 + 12 \sqrt{7}$

Decimal Form:

$46.74901573 \dots$