Approximating Square Roots

A 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 approximate a square root, find two perfect squares between which the number lies. For example, to approximate $$\text{√}8$$ , note that 4 (2^2) and 9 (3^2) are perfect squares around it. Thus, $$\text{√}8$$ is between 2 and 3.

The square root of 0.25 is 0.5, because 0.5 x 0.5 = 0.25.

0.7 as a fraction is $$\frac{7}{10}$$ .

0.5 as a fraction is $$\frac{1}{2}$$ .

The square root of 16 is 4, because 4 x 4 = 16.

A number is a perfect square if its square root is an integer. For example, 25 is a perfect square because $$\text{√}25 = 5$$ , which is an integer.

The approximate value of $$\text{√}10$$ is about 3.16, since it lies between 3 (3^2 = 9) and 4 (4^2 = 16).

The square root of 1 is 1, because 1 x 1 = 1.

To simplify a square root, factor the number into its prime factors and pair them. For example, $$\text{√}18 = \text{√}(9 \times 2) = 3\text{√}2$$ .