Simplify the Radical Expression square root of 175+8 square root of 7

$\sqrt{175} + 8 \sqrt{7}$

Simplify each term.

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$\sqrt{25 (7)} + 8 \sqrt{7}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 7} + 8 \sqrt{7}$

Pull terms out from under the radical.

$| 5 | \sqrt{7} + 8 \sqrt{7}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$5 \sqrt{7} + 8 \sqrt{7}$

Add $5 \sqrt{7}$ and $8 \sqrt{7}$ .

$13 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{7}$

Decimal Form:

$34.39476704 \dots$