Use square root and cube root symbols to represent solutions to equations

What you'll learn

1. Use the square root symbol to represent solutions to equations of the form x^2 = p, distinguishing between the principal root sqrtp and the two solutions x = +/-sqrtp
2. Use the cube root symbol to represent solutions to equations of the form x^3 = p, recognizing that each such equation has exactly one real solution x = cbrtp
3. Evaluate square roots of perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144) and cube roots of perfect cubes (1, 8, 27, 64, 125) from memory
4. Evaluate square roots and cube roots of positive rational numbers that are perfect squares or perfect cubes, including fractions such as sqrt(1/4) = 1/2 and cbrt(1/8) = 1/2
5. Identify sqrt2 as irrational and explain that square roots of non-perfect-squares (such as sqrt3, sqrt5, sqrt7) are irrational numbers whose decimal expansions neither terminate nor repeat

Prerequisites

• Know that numbers that are not rational are called irrational