Question

go step by step to reduce the radical. \\(sqrt{160}\\) \\(sqrt{square} sqrt{square}\\)

Explanation:

Step1: Factor out perfect square

Find the largest perfect square factor of 160. The largest perfect square that divides 160 is 16, since $16 \times 10 = 160$.
$\sqrt{160} = \sqrt{16 \times 10}$

Step2: Split radical using product rule

Apply the radical product property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.
$\sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10}$

Step3: Simplify perfect square radical

Calculate the square root of 16.
$\sqrt{16} = 4$

Answer:

$\sqrt{160} = 4\sqrt{10}$
(The filled blanks are $\sqrt{16}$ and $\sqrt{10}$)