Question

65 give all possible roots to the radical \\(\sqrt{81}\\)

Explanation:

Step1: Recall square root definition

The square root of a number \( x \) is a value \( y \) such that \( y^2 = x \). For \( \sqrt{81} \), we consider both positive and negative roots because \( (\pm 9)^2 = 81 \).

Step2: Identify possible roots

Since \( 9^2 = 81 \) and \( (-9)^2 = 81 \), the possible roots of \( \sqrt{81} \) (when considering all real roots that satisfy the square - root relationship) are \( 9 \) and \( -9 \). But when we talk about the principal square root (the non - negative square root), \( \sqrt{81}=9 \). However, the question says "ALL possible roots" for the radical in the sense of numbers whose square is 81. So the possible roots are \( 9 \) and \( -9 \).

Answer:

\( 9 \) and \( -9 \)