Square and cube roots

Find neighbouring integers whose squares surround the radicand: a² < n < (a + 1)². Then a < √n < a + 1. For example, 16 < 20 < 25, so 4 < √20 < 5.

If b is nonnegative, compare n with b²: the same comparison holds between √n and b. For example, 20 < 25 = 5², so √20 < 5.

The cube root ∛n is the number whose cube equals n. For example, ∛27 = 3 because 3 × 3 × 3 = 27.

Evaluate the roots and divide the first by the second. For a ≥ 0 and b > 0, √a ÷ √b = √(a ÷ b). For example, √36 ÷ √4 = 6 ÷ 2 = 3.

The cube root ∛n is the number whose cube equals n. For example, ∛27 = 3 because 3 × 3 × 3 = 27.

Evaluate both principal roots and multiply their values. For nonnegative a and b, √a × √b = √(a × b). For example, √9 × √16 = 3 × 4 = 12.

The principal square root √n is the nonnegative number whose square equals n. For example, √49 = 7 because 7² = 49. Although (−7)² is also 49, √ denotes the nonnegative value.

Evaluate the roots and divide the first by the second. For a ≥ 0 and b > 0, √a ÷ √b = √(a ÷ b). For example, √36 ÷ √4 = 6 ÷ 2 = 3.

The principal square root √n is the nonnegative number whose square equals n. For example, √49 = 7 because 7² = 49. Although (−7)² is also 49, √ denotes the nonnegative value.