What is the approximate value of the square root of 7?

The approximate value of the square root of 7 is about 2.65. To arrive at this value, one can consider the perfect squares close to 7. The perfect squares of 2 and 3 are 4 and 9, respectively; thus, the square root of 7 must fall between 2 and 3.

When estimating, it helps to determine that:

• The square of 2.5 is (2.5^2 = 6.25)

• The square of 2.6 is (2.6^2 = 6.76)

• The square of 2.7 is (2.7^2 = 7.29)

Since (6.76) is less than (7) and (7.29) is greater than (7), it follows that the square root of 7 lies between 2.6 and 2.7. Thus, 2.65 serves as a reasonable approximation because it is centrally located between these two values.

This process illustrates the logical steps in estimating square roots using nearby perfect squares, leading to the conclusion that the square root of 7 is indeed approximately 2.