Question

question
go step by step to reduce the radical.
\sqrt{72}
\sqrt{\square} \sqrt{\square}

Explanation:

Step1: Factor 72 into perfect square and other

We know that \( 72 = 36\times2 \), where 36 is a perfect square. So, \( \sqrt{72}=\sqrt{36\times2} \).

Step2: Use property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0,b\geq0 \)), we get \( \sqrt{36\times2}=\sqrt{36}\times\sqrt{2} \).

Step3: Simplify \( \sqrt{36} \)

Since \( 6^2 = 36 \), \( \sqrt{36}=6 \). So, \( \sqrt{72}=6\sqrt{2} \). But for the given form \( \sqrt{\square}\sqrt{\square} \), we have \( \sqrt{36}\sqrt{2} \) (or \( \sqrt{2}\sqrt{36} \)).

Answer:

The first square is 36 and the second square is 2 (or vice - versa), so \( \sqrt{36}\sqrt{2} \) (or \( \sqrt{2}\sqrt{36} \)) and the simplified radical is \( 6\sqrt{2} \). For the blanks in \( \sqrt{\square}\sqrt{\square} \), the answer is 36 and 2 (in either order).