Final answer:
The square root of a number between 3 and 4 will be a non-integer value more than 3 but less than 4. Without a precise location on the number line, an exact value can't be given, but typically would be estimated or calculated.
Step-by-step explanation:
The student is asking about the square root of a number that lies between 3 and 4. Since each whole number has a definite square root, and here we are interested in a number between 3 and 4, we are looking for a non-integer square root. Now, 3² is 9 and 4² is 16. The square root in question would be more than 3 but less than 4.
One way to estimate this is to recognize that the number line is linear, so the square root we are looking for would be roughly halfway between the square roots of 9 and 16 if it is halfway between 3 and 4. For a more precise value, one might need to resort to a calculator or approximation methods such as guessing and checking, or using the property that (3.5)² is slightly more than 12 which is close to our target area on the number line.
However, without specific information of where the number lies between 3 and 4 on the number line, we cannot identify the exact square root. It is important to be comfortable with the concept of square roots as they are frequently encountered in various mathematical and practical problems, such as calculating the hypotenuse of a right-angled triangle or understanding the properties of exponents and powers, including when they are expressed as fractions such as 3¹.⁷.