Question

simplify.
√54

Explanation:

Step1: Factor 54 into prime factors

We know that \( 54 = 9\times6 \), and \( 9 = 3^2 \) (a perfect square), so we can rewrite \( \sqrt{54} \) as \( \sqrt{9\times6} \).

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

Applying this property, \( \sqrt{9\times6}=\sqrt{9}\times\sqrt{6} \).

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

Since \( \sqrt{9} = 3 \) (because \( 3^2 = 9 \)), we substitute this back to get \( 3\sqrt{6} \).

Answer:

\( 3\sqrt{6} \)