To determine between which two consecutive whole numbers the square root of 82 lies, we start by finding the approximate value of [tex]\(\sqrt{82}\)[/tex].
1. Calculate the square root of 82. The approximate value of [tex]\(\sqrt{82}\)[/tex] is 9.055385138137417.
2. Identify the two consecutive whole numbers surrounding this decimal value. Since 9.055385138137417 is more than 9 and less than 10, the two consecutive whole numbers between which [tex]\(\sqrt{82}\)[/tex] lies are 9 and 10.
So, [tex]\(\sqrt{82}\)[/tex] is between 9 and 10 because 9 is the integer part of the square root of 82, and adding 1 to 9 gives us 10, ensuring that 9 < [tex]\(\sqrt{82}\)[/tex] < 10. Thus, [tex]\(\sqrt{82}\)[/tex] is between the two whole numbers 9 and 10.
