Question

question
go step by step to reduce the radical.
\sqrt{243}
\sqrt{\boxed{1}} \sqrt{\boxed{}}

Explanation:

Step1: Factor 243 into perfect square and other

We know that \( 243 = 81\times3 \), where \( 81 \) is a perfect square (\( 9^2 \)). So we can rewrite \( \sqrt{243} \) as \( \sqrt{81\times3} \).

Step2: Use radical property \( \sqrt{ab}=\sqrt{a}\sqrt{b} \)

Using the property \( \sqrt{ab}=\sqrt{a}\sqrt{b} \) (for \( a\geq0,b\geq0 \)), we get \( \sqrt{81\times3}=\sqrt{81}\times\sqrt{3} \).

Step3: Simplify \( \sqrt{81} \)

Since \( 9^2 = 81 \), \( \sqrt{81}=9 \). So \( \sqrt{81}\times\sqrt{3}=9\sqrt{3} \). But for the given form \( \sqrt{\square}\sqrt{\square} \), we have \( \sqrt{81}\sqrt{3} \) (or in the boxes, the first box is 81 and the second is 3).

Answer:

The first box is \( 81 \) and the second box is \( 3 \), so the radical reduced as \( \sqrt{81}\sqrt{3} \) (and further simplified to \( 9\sqrt{3} \)).