Question

simplify \\(\sqrt{63x}\\)

Explanation:

Step1: Factor the radicand

Factor 63 into its prime factors: \( 63 = 9\times7 \), where 9 is a perfect square. So, \( \sqrt{63x}=\sqrt{9\times7\times x} \).

Step2: Apply the square - root property

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0,b\geq0 \)), we can split the square root: \( \sqrt{9\times7\times x}=\sqrt{9}\times\sqrt{7x} \).
Since \( \sqrt{9} = 3 \), we get \( 3\sqrt{7x} \).

Answer:

\( 3\sqrt{7x} \)