Between which two whole numbers is \sqrt{7}?

Answer

To determine which two whole numbers \sqrt{7} lies between, we need to find the nearest perfect squares that are less than and greater than 7. The perfect squares are 1, 4, 9, 16, etc. Specifically, 4 is 2 squared (2^2 = 4) and 9 is 3 squared (3^2 = 9). Since 7 is between 4 and 9 (4 < 7 < 9), taking the square root of all parts gives \sqrt{4} < \sqrt{7} < \sqrt{9}, which simplifies to 2 < \sqrt{7} < 3. Therefore, \sqrt{7} lies between the whole numbers 2 and 3.