Question

go step by step to reduce the radical.
$sqrt{176}$
$sqrt{square}$ $sqrt{square}$
try

Explanation:

Step1: Factor out perfect square

Find the largest perfect square factor of 176. The largest perfect square that divides 176 is 16, since $16 \times 11 = 176$.
$\sqrt{176} = \sqrt{16 \times 11}$

Step2: Split radical using property

Use the radical property $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ where $a \geq 0, b \geq 0$.
$\sqrt{16 \times 11} = \sqrt{16} \times \sqrt{11}$

Step3: Simplify perfect square radical

Calculate $\sqrt{16} = 4$.
$\sqrt{16} \times \sqrt{11} = 4\sqrt{11}$

Answer:

The split form is $\sqrt{16} \sqrt{11}$, and the simplified radical is $4\sqrt{11}$