To find the principal square root of [tex]\( 81 \)[/tex], you can follow these steps:
1. Recall the definition of the principal square root. The principal square root of a non-negative number [tex]\( x \)[/tex] is the non-negative number [tex]\( y \)[/tex] such that [tex]\( y^2 = x \)[/tex].
2. Identify the number whose principal square root you need to find. In this case, it is [tex]\( 81 \)[/tex].
3. Determine a number [tex]\( y \)[/tex] such that [tex]\( y^2 = 81 \)[/tex].
4. Through knowledge of square numbers, recognize that [tex]\( 9^2 = 81 \)[/tex].
5. Therefore, [tex]\( 9 \)[/tex] is the principal square root of [tex]\( 81 \)[/tex].
So, the principal square root of [tex]\( 81 \)[/tex] is [tex]\( 9.0 \)[/tex].
