Question

simplifying radicals (guided)
this is the only question in this section.
question
go step by step to reduce the radical.
$sqrt{243}$
$sqrt{square} sqrt{square}$
try

Explanation:

Step1: Factor out perfect square

Find the largest perfect square factor of 243. The largest perfect square that divides 243 is 81, since $81 \times 3 = 243$.
$\sqrt{243} = \sqrt{81 \times 3}$

Step2: Apply radical product rule

Use the property $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ to split the radical.
$\sqrt{81 \times 3} = \sqrt{81} \times \sqrt{3}$

Step3: Simplify perfect square radical

Calculate $\sqrt{81}$, which equals 9.
$\sqrt{81} \times \sqrt{3} = 9\sqrt{3}$

Answer:

$\sqrt{81}\sqrt{3}$ (intermediate step), simplified final form: $9\sqrt{3}$