Estimating Square Roots

A non-perfect square is a number that cannot be expressed as the square of an integer. For example, 2, 3, 5, and 6 are non-perfect squares.

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 x 3 = 9.

To estimate the square root of a non-perfect square, find the two perfect squares it lies between and then approximate the value.

The perfect squares between 60 are 49 (7^2) and 64 (8^2). Therefore, $$\text{7 and 8}$$ are the two numbers.

The best estimation for $$\text{sqrt(6)}$$ is 2.4, as it lies between the perfect squares 4 (2^2) and 9 (3^2).

The perfect squares between 111 are 100 (10^2) and 121 (11^2). Therefore, $$\text{10 and 11}$$ are the two numbers.

The best estimation for $$\text{sqrt(110)}$$ is 10.5, as it lies between the perfect squares 100 (10^2) and 121 (11^2).

The perfect squares between 15 are 9 (3^2) and 16 (4^2). Therefore, $$\text{3 and 4}$$ are the two numbers.

The best estimation for $$\text{sqrt(15)}$$ is 3.9, as it lies between the perfect squares 9 (3^2) and 16 (4^2).

The square root of 49 is 7, since 7 x 7 = 49.