Question

Bill has a secret number, B, and wants help finding its square root. What two integers must square root B be between?

a) 36 < square root B < 49
b) 7 < square root B < 8
c) 6 < square root B < 7
d) 6 < square root B < 8

Answer 1

d) 6 < square root B < 8 it's the appropriate range for the square root of B.

Step-by-step explanation:

The square root of B must fall between 6 and 8 inclusively. This range is denoted as "6 < square root B < 8" which is option d.

To determine the correct answer, consider the nature of square roots. A square root represents a number that, when multiplied by itself, results in the given number. In this case, if B is squared, the result will fall between the squares of 6 and 8. Squaring 6 gives 36, and squaring 8 gives 64. Therefore, if B falls between these values, its square root must fall between the square roots of 36 and 64, which are 6 and 8 respectively.

The range 6 < square root B < 8 encompasses all possible integers between the square roots of 36 and 64, satisfying the condition for B's square root. Therefore, it's the appropriate range for the square root of B.

This solution considers the fundamental concept that a square root falls between the square roots of consecutive perfect squares. Thus, the answer provides the accurate range within which the square root of B must lie to satisfy the condition given.