Question

what value can be placed in front of the radical symbol to make this statement true?\\(\sqrt{54} = \square\sqrt{6}\\)

Explanation:

Step1: Factor 54 into 6 and 9

We know that \( 54 = 6\times9 \), so we can rewrite \( \sqrt{54} \) as \( \sqrt{6\times9} \).

Step2: Use the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0, b\geq0 \))

Applying this property, \( \sqrt{6\times9}=\sqrt{6}\times\sqrt{9} \).

Step3: Simplify \( \sqrt{9} \)

Since \( \sqrt{9} = 3 \), we have \( \sqrt{6}\times\sqrt{9}=3\sqrt{6} \). So the value in the box should be 3.

Answer:

3